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2011 Problem Solving …

2011 Problem Solving
(Problem, Hints, Solution and Answer)

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  • 1. 2011 Calendar Problem Solving
  • 2. LORETO MORALES MARIELLA ALEXES ROMBAOA MECHILLE LACUESTA DIAN MENESES CAROLYN GRANDEFree Powerpoint Templates JOYCE ESTEBAN MYRELL
  • 3. Click thered arrow to open theproblemonths
  • 4. 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1516 17 18 19 20 21 2223 24 25 26 27 28 2930 31 BACK TO LIST
  • 5. FEBRUARY 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 56 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 BACK TO LIST
  • 6. MARCH 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  • 7. APRIL 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 910 11 12 13 14 15 1617 18 19 20 21 22 2324 25 26 27 28 29 30 BACK TO LIST
  • 8. MAY 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 12 13 1415 16 17 18 19 20 2122 23 24 25 26 27 2829 30 31 BACK TO LIST
  • 9. JUNE 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 BACK TO LIST
  • 10. JULY 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  • 11. AUGUST 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  • 12. SEPTEMBER 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 BACK TO LIST
  • 13. 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  • 14. NOVEMBER 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 BACK TO LIST
  • 15. DECEMBER 2011SUN MON TUE WED THU FRI SAT 1 2 3 4 5 6 7 8 9 10 11 1213 14 15 16 17 18 1920 21 22 23 24 25 2627 28 29 30 31 BACK TO LIST
  • 16. Batman has been imprisoned by the Riddler. To escape he must find the quickest way to move the tower ofplutonium disks from one post to another so that the disks have the same arrangement as on the original post. Hemay move only one disk at a time. What is the minimum number of moves he mustmake in order to move the ten disk tower and have it appear the same? Hint and answer
  • 17. Hints:1) Batman can put all disks on one post and then switch tothe second post in 20 moves. How would he reduce his task?Answer: The quickest way is to move each diskonto the first post except for the last disk -> which is 9moves. Then move the last disk to the secondpost which is one move. Then move each of the disks on the firstpost to the second post which is an additional 9 moves. 9 + 9 + 1 = 19 moves BACK
  • 18. Seth and Bob each began reading a HardyBoys book today. If Seth reads 8 pages eachday and Bob reads 5 pages each day, whatpage will Bob be reading when Seth isreading page 56? (Hint: Complete the table.) Day Seths Page Bobs Page 1 8 5 2 16 10 3 24 15 Hint and answer
  • 19. Day Seths Page Bobs Page 1 8 5 2 16 10 3 24 15 4 32 20 5 40 25 6 48 30 7 56 35BACK
  • 20. How many differentcubes can you make ifeach face of a givencube has a lineconnecting the centerpoints of two oppositeedges?Hint and answer
  • 21. Hint:1) There are three sets of opposing faces that will be split into four. BACK 23 = 8 cubes
  • 22. Find the number of faces, edges and vertices on the figure shown.•What would this figure be called?•What would the two figures contained in it be called? Hint and answer
  • 23. Hints:NONE!Answer: 17 edges 9 faces 10 verticesPentagonal Prism contains a rectangular prismand a right trianglular prism. BACK
  • 24. Scientists have just discovered people on Neptune. There are 3villages, 2 cities and 1 super city on Neptune. These are thepopulations in 1994 and 1996. 1994 1996 Eilosa 129 204 Vertu 308 292 Pridi 90 50 Dedrun 500 600 Antran 700 693 Maran 1200 1500List the places in order of increasing size in 1994 and 1996.In which year was the population of the planet greater? Hint and answer
  • 25. Hints:Sum each column!Solution and Answer: 1994 1996 Eilosa 129 204 Vertu 308 292 Pridi 90 50 Dedrun 500 600 Antran 700 693 Maran 1200 1500 ----------------- 2927 3339 3339 - 2927 = 412 therefore the population in 96 is greater BACK
  • 26. Can you find allof the spokes? Adigit on a hubdenotes thenumber ofspokes that meetthere. Spokesnever cross andin the endeverything willbe connected. Answer
  • 27. Answer BACK
  • 28. A farmer grows 252 kilograms of apples. He sells them to a grocer who divides them into 5 kilogram and 2 kilogram bags. If the grocer uses the same number of 5 kg bags as 2kg bags, then how many bags did he use in all?Need A Hint? And Answer
  • 29. Hints:1) Let x = total number of bagsAnswer: Let x = total number of bags5(1/2 x) + 2 (1/2 x) = 252 2.5x + 1x = 252 3.5x=252 x = 72 bags. BACK
  • 30. This is a turtle graphics problem.A bug is walking across the doorstep of a house. When hestarts out he is facing the house at the opposite side of thedoorstep. If he goes 3 units left, 1 unit right, 2 units left, 8units left, what will the bug have to do to get back wherehe started as quickly as possible without retracing hissteps? Hint and answer
  • 31. Hints:1) Remember, you face the direction you go!2) Draw a diagram. HOUSE Answer: 1 unit left and 3 units left. BACK
  • 32. Three ducks and two ducklingsweigh 32 kg. Four ducks and threeducklings weigh 44kg. All ducksweigh the same and all ducklingsweigh the same. What is the weightof two ducks and one duckling?Hint and answer
  • 33. Hints: 1) Set up two equationsAnswer: Let D = the weight of one duck d = the weight of one ducklingSolve:(3D + 2d = 32)*3 ------> 9D + 6d = 96 (4D + 3d = 44)*2 ------> 8D + 6d = 88 ______________ 1D + 0d = 8 -----> D = 8 Substitute to solve for d: 4D + 3d = 444(8) + 3d = 44 32 + 3d = 44 3d = 12 d=4Thus, 2D + d = 2(8) + 4 = 20 kgs. BACK
  • 34. It takes one man one day to dig a 2m x 2m x2m hole. How long does it take 3 menworking at the same rate to dig a 4m x 4m x4m hole? If you can finish these problem, youll be smarter than I am.Hint and answer
  • 35. Hints:1) Find rate of one manAnswer: Let x = rate of one man = 23 m3/ 1 day = 8m3/day 3x = rate of three men = 3(8m3/day) = 24m3/dayVolume to be shoveled = 64m3Therefore, it would take three men 64m3/(24m3/day) = 2 2/3 days BACK
  • 36. Hints: 1) Try putting addition signs between the different numbers. 2) Try this example: ANSWER:1) 9+8+7+65+4+3+2+1 = 99 -> 7 addition signs.2) 9+8+7+6+5+43+21 = 99 -> 6 addition signs. BACK
  • 37. A 800 seat multiplex is divided into 3 theatres. There are 270 seats in Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many seats are in Theatre 2?Hint and answer
  • 38. Hints:1) Let x = seats in Theatre 3. Then number of seats in Theatre 2= x + 150 seats.Answer: Let x = number of seats in Theatre 3 T1 = Theatre 1 = 270 seats T2 = Theatre 2 = 150 + x T1 + T2 + T3 = 800 seats 270 + (150 + x) + x = 800 420 + 2x = 800 x = 190If there are x = 190 seats in theatre 3,then Theatre 2 has150 + 190 = 340 seats BACK
  • 39. HINT:1) Draw a diagram -> use least common multiples. x = Frog 1 o = Frog 2ANSWER:• How many numbers between 1 and 18 are multiples of 2 and 3?• 6, 12, 18[ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o][ ][o][x][o][ ][x/o]• 1 2 3• There will only be 3 lily pads that both frogs jump on• - Number 6, 12 and 18. BACK
  • 40. ANSWER: (3/10)*? = 24 and 24/(3/10) = 80. Aunt Helen is 80 years old. BACK
  • 41. Question: It takes one man one day to dig a 2m x 2m x 2m hole. How long does it take 3 men working at the same rate to dig a 4m x 4m x 4m hole?Hint and answer
  • 42. Hint: Find rate of one manAnswer:Let x = rate of one man = 23 m3/1day = 8m3/day 3x = rate of three men = 3(8m3/day) = 24m3/day Volume to be shoveled = 64m3 Therefore, it would take three men 64m3/(24m3/day) = 2 2/3 days BACK
  • 43. Hint and answer
  • 44. Hint: To find the answers, multiples of 2.Answer: To find the multiples of a number, multiply that number by 0, 1, 2, 3, 4, 5…… 2 (0) = 0 2 (1) = 2 2(2) = 4 2 (4) = 8 2 (5) = 10 The next 3 garbage bins are placed near the 6th, 8th, and 10th houses. BACK
  • 45. Question: A farmer grows 252 kilograms of apples. He sells them to a grocer who divides them into 5 kilogram and 2 kilogram bags. If the grocer uses the same number of 5 kg bags as 2kg bags, then how many bags did he use in all?Hint and answer
  • 46. Hint: Let x = total number ofbagsAnswer: Let x = total number of bags 5(1/2 x) + 2 (1/2 x) = 252 2.5x + 1x = 252 3.5x = 252 x = 72 bags. BACK
  • 47. Question:A 800 seat multiplex is divided into 3 theatres. There are 270 seats in Theatre 1, and there are 150 more seats in Theatre 2 than in Theatre 3. How many seats are in Theatre 2?Hint and answer
  • 48. Hint :Let x = seats in Theatre 3. Then number of seats inTheatre 2 = x + 150 seats .Answer: Let x = no. of seats in Theatre 3 T1 = Theatre 1 = 270 seats t2 = Theatre 2 = 150 + x T1 + T2 + T3 = 800 seats270 + (150 + x) + x = 800 420 + 2x = 800 x = 190 If there are x = 190 seats in theatre 3, thenTheatre 2 has150 + 190 = 340 seats BACK
  • 49. Question: In 1969 the price of 5 kilograms of flour was P0.75. In 1970 the price was increased 15 percent. In 1971, the 1970 price was decreased by 5 percent. What was the price of 5 kilograms of flour in 1971?Hint and answer
  • 50. Hint: Let 1970 cost = (P0.75)*1.15Answer: If the price of 5 Kg of flour in 1969 = P0.75, then 1970 = P0.75 x 1.15 = P0.8625 1971 = (PO0.75 x 1.15) x .95 = P0.82 BACK
  • 51. Question: A rectangular sheetof wood has four smallsquares removed. It isthen cut to make a boxthat is 5cm by 4cm witha volume of 60cm3.(Four pieces of size A4are removed.) Find theoriginal area of thesheet of wood.Hint and answer
  • 52. Hint: Open top boxAnswer: l x h x w = 60 h(5)(4) = 60 h=3A(1) = 4 x 5 = 202A(2) = 2(3)(5) = 302A(3) = 2(3)(4) = 244A(4) = 4(3)(3) = 36 Total A = A(1) + 2A(2) + 2A(3) + 4A(4) = 20 + 30 + 24 + 36 = 110cm2 BACK
  • 53. Question: Mary has $50.00. She goes to the mall and buys lipstick and then she buys shampoo, which is half the price of the lipstick. She then spends half of what she has left on a purse, leaving her with $15.00. How much did the shampoo cost? How much did the lipstick cost?Hint and answer
  • 54. Hint: Purse cost $15.00Answer: Let x = price of lipstick 1/2 x = price of shampoo Cost of lipstick AND shampoo,combined = x + 1/2xMoney spent on lipstick and shampoo combined: $50.00 - ($15.00)*2 = $20.00Therefore, x + 1/2 x = $20.00 1.5x = $20.00 x = $13.33 Lipstick cost: x = $13.33 Shampoo cost: 1/2 x = 1/2 * $13.33 = $6.67 BACK
  • 55. Question: Stephanie had P40.00 savings. Her mother gave her another P30.00 and her grandmother gave her P10.00 to buy a pair of cleats. The pair of cleats Stephanie wants costs P54.99. If Stephanie buys the cleats at a no TAX sale, write an equation using a variable to describe the amount of money that Stephanie will have to contribute from her savings. Solve for the variable.Hint and answer
  • 56. Hint :Stephanie spends all of money from her mother and grandmotherAnswer:Let x = Stephanie‘s contribution.P30.00 + P10.00 = P40.00P40.00 + x = P54.99 x = P14.99 BACK
  • 57. Question: Given a rectangular prism. If the sides of the rectangle A have the same ratio to each other as the sides of rectangle B, then what is (a) The surface area of the prism? (b) The volume of the prism? Hint and answer
  • 58. Hint: 1.Find length of x first 2.Find area of A and area of BAnswer: Dimensions B: 5/8 = 8/x 64 = 5x 12.8 = x (a) Surface Area = 2 * Area A + 2 * Area B + Area (top) + Area (bottom) = 2(8*5) + 2(8*12.8) + 2(5*12.8) = 412.8(b) Volume = l x w x h = (12.8)(5)(8) = 512 BACK
  • 59. Question: The trails in a park resemble the following diagram. Find the total length of the trails, given that all the circles have the same area and circle 2 is tangent to the midpoint of L.Hint and answer
  • 60. Hint: W = diameter = 2rAnswer:2r + 3L + 3w + 3pi*a = 2(10) + 3(100) + 3(20)+3pi(20) = 568.50m(2r+L) + 2L + 3W + 3piW = (2(10)+40) + 2(40) + 3(20) 3pi(20) = 388.50 m BACK
  • 61. Question:The rent-a-stall horse barn has stalls for 1000 horses. Forty percent of the stalls are for ponies. On Tuesday, there were 200 ponies and a bunch of quarter horses at the horse barn. The horse barn was 75 percent full.How many quarter horses were in the stalls?Hint and answer
  • 62. Hint: Find total number of stalls filledAnswer: 75% full = 75% * 1000 horses = 750 horsesIf there are 200 ponies, there must be (750 - 200) = 550 quarter horses BACK
  • 63. Question: A rectangular chalk board is 3 times as long as it is wide. If it were 3 meters shorter and 3 meters wider, it would be square. What are the dimensions of the chalk board?Hint and answer
  • 64. Hint: Sides of square are equalAnswer:Let x= width of chalkboard Therefore, 3x = length of chalkboardSince sides of square are equal, 3x - 3 = x + 3 2x = 6 x=3 Dimensions of chalkboard: width = x = 3 meters widelength = 3x = 9 meters long BACK
  • 65. Question: Three people share a car for a period of one year and the mean number of kilometers traveled by each person is 152 per month. How many kilometers will be traveled in one year?Hint and answer
  • 66. Find total number of kilometersHint:traveled per monthAnswer: 3 x 152km/month x 12 months/year = 5472 km/year BACK
  • 67. Question:A car dealer claims that by buying a new car Mike will pay 1/5 less for gas then he pays for the car he currently drives. If the car Mike currently drives costs 1/6 less to gas up than Daves car, and Dave pays $700.00 per year, what will it cost Mike to put gas in a new car for one year (assuming all cars will be traveling the same distance)?Hint and answer
  • 68. Hint: 1/6 less than 700 = 5/6(700)Answer: (700.00)(5/6)(4/5) = $466.67 BACK
  • 69. Question:A side of the equilateral triangle A is twice the length of a side of triangle B.How many triangle B will fit into triangle A?Hint and answer
  • 70. Hint: Draw triangle A and fit triangle Bs into it 2) How manytimes will the area of B divide the area of A?Answer: 4 triangles BACK
  • 71. Question: A storage facility has space for 225 - 8 liter boxes and 515 - 27 liter boxes. What is the volume of the facility? What percent of the total volume is filled by 150 of the 8 liter boxes and 5 of the 27 liter boxes?Hint and answer
  • 72. Hint: Total volume = 8 * 225 + 27 *515Answer:a) 225*8litres+515*27liters=TotalVol 15705 litres = 15.705 kilolitresb) [(150*8 + 5*27) / 15705] x 100 percent = 8.500 percent. BACK
  • 73. Question: Marvins Taxi Service charges $0.30 for the first kilometer and $0.05 for each additional km. If the cab fare was $3.20, how far did the Taxi go?Hint and answer
  • 74. Hints:Total volume = 8 * 225 + 27 * 515Answer:Cost of first kilometer = $0.30 Total cost of additional kilometers = (3.20 - 0.30) = 2.90Total number of kilometers = 1 +($2.90/$0.05) = 1 + 58 = 59 km BACK
  • 75. Question: What fraction of this square is shaded?Hint and answer
  • 76. Hints:Use table to calculate total amount of gas used by eachpersonAnswer:Total area of square = (1/4 + 3/4)*(2/3 + 1/3) =1*1 =1Shaded area = (2/3 * 3/4) = 0.5Fraction of Total area shaded =0.5/1 = 50% BACK
  • 77. Question: The number of hours left in a day on Mars was 1/4 of the number of hours that had already passed. How many hours were left in the day? Day on Mars 40 hours.Hint and answer
  • 78. Hints:Total area of square = (1/4 + 3/4) * (2/3 + 1/3) = 1*1=1 Answer:Let x = the number of hours that had already passed1/4 x = the number of hours remaining IF total number of hours in a day = 40, THEN x + 1/4x = 40 5/4x = 40 160x = 5 x = 160/5 x = 32Hours remaining = 1/4 x = 1/4(32) =8 BACK
  • 79. Question: A cereal company decided to increase the height of its boxes by 30 percent and reduce the width in order to maintain the same volume. If initially, length 20cm height 40cm width = 30cm What will the new height and width be if length stays the same?Hint and answer
  • 80. Hints:An increase in the height h by 30% is (1+0.3)h=1.3h.Answer: Volume = l * w * h = (20)(30)(40)cm3 = 24000cm3New height = initial h + 0.3h = 1.3h = 1.3 * 40cm = 52 cmIF height = 52 cm, solve for w:Volume = l * w * h 24000 cm3 = (20cm)(w)(52cm) 24000 cm3 = 1040(w)cm2 w = 23.08 cm BACK
  • 81. Question: of times a dog barks depends on the The number number of cars passing. How many cars have passed when a dog barks 22 times? How many barks for 5 cars? Cars Barks ------+------- 6 | 4 7 | 7 8 | 10 9 | 13 10 | 16 Hint and answer
  • 82. Hint: Look for a pattern: Begin at the bottom of the column - subtractthe first number from the next number and compare to the difference of thecorresponding two numbers in the other column.Answer: Pattern: 6 - 13 = 3 10 - 7 = 3 0-9=1 8-7=1 3 barks for 1 car Therefore, 22 barks for 12 cars. BACK
  • 83. Hints: Divide the face of the clock into three parts with two lines so that the sum of the numbers in the three parts are equal. 1) Divide the clock into three parts with two lines. Add up the numbers in each section. Are they equal? If not try again.Answer: 26+26+26 = 78 BACK
  • 84. PROBLEM  According to experts the first 4 moves in a chess game can be played in 197299 totally different ways. If it takes 30 seconds to make one move, how long would it take one player to try every possible set of 4 moves?Hint and answer
  • 85. Hints: 1) 197299 sets of four moves 2) Each of the 4 moves takes 30 seconds.Answer: 30 seconds * 4 * 197299 = 23675880 seconds. BACK
  • 86. PROBLEM  A man has to be at work by 9:00 a.m. and it takes him 15 minutes to get dressed, 20 minutes to eat and 35 minutes to walk to work. What time should he get up?Hint and answer
  • 87. Hints: 1) Add up time required 2) Subtract this time from the time he has to be at work. Eg. 9:00 - 20 min= 8:40Answer: 9 hours - (15 + 20 + 35) 9 hours - 70 minutes 7 hours + 120 minutes - 70 minutes = 7 hours and 50 minutes = 7:50 AM BACK
  • 88. Question: There are 360 degrees in a circle. If the population of various planets are represented by a circle graph, match the percentage of the population of the solar system that is found on each planet with an area on the graph. Planet Percent -----------+---------- Earth 27.78% Mars 20.80 Venus 1 6.67 Jupiter 2.78 Mercury 2.78 Neptune 6.11 Pluto 1.67Hint and answer
  • 89. Hint: You will only find 99.98 percent Answer: BACK
  • 90. Question: A tire shop that sells only one size of tire, .75 meters in diameter, decides to sell tires for big rigs that are 1.5 meters in diameter. If the cost of the .75 meter tires is $100.00 for four, how much will it cost for the 18 tires required for a big rig? Prices increase proportionally with size.Hint and answer
  • 91. Hints:1) Find the cost of a .75 m tire2) Use to find cost of big rig tireAnswer: Let x = price for each big rig tire Size Price/tire 0.75m $100/4 = $25.00 each 1.5m xSolve for x: 0.75m/$25.00 = 1.5/x 0.75x = 1.5 * $25.00 0.75x = $37.50x = $50.00/tireTherefore: Price for 18 tires = 18($50.00) = $900.00 BACK
  • 92. Question:Four friends buy a pizza that costs $20.00. Each person contributes a the following amount of money. Jane $5.00 Mike 8.00 Mary 3.00 Joe 4.00Each person will eat an amount of pizza proportional to the amount of money they paid.1)Draw a circle graph that represents the amount each eat.2)Draw the circle graph if Mike only eats half of his pizza and gives half of what he has left to Mary.Hint and answer
  • 93. Hints: Find the proportion of money paid by each personAnswer: Cost of Pizza=$20.00 PROPORTIONS:Jane:520=1/4 Jane: 5/20 =1/4Mike:8/20=4/10=2/5 Mike: 8/20-4/20 = 4/20 = 1/ 5Mary:3/20 Mary: 3/20 + 4/20 = 7/20Joe: 4/20 = 15 Joe: 4/20 = 1/5 BACK
  • 94. Question: A boy ate 100 cookies in five days. Each day he ate 6 more than the day before. How many cookies did he eat on the first day?Hint and answer
  • 95. Hint: Let x = the number of cookies eaten the first dayAnswer:Let x = the number of cookies eaten on the first day Cookies Eaten Day 1 x 2 x + 1(6) 3 x + 2(6) 4 x + 3(6) 5 x + 4(6) TOTAL 5x + 10(6) = 100 cookies Solve for x: 5x + 10(6) = 100 5x + 60 = 100 5x = 40 x=8 BACK
  • 96. Question: M and N are the midpoints of the sides of a square. What is the ratio of the area of triangle AMN to the area of the complete square?Hint and answer
  • 97. Hints:Triangle AMN: base = height = 1/2 sAnswer: Since s = sides of square Area square = s^2 Area triangle = (1/2)b*h = (1/2)(1/2 s)(1/2 s) = 1/8 s^2Ratio = Area triangle/Area square = 1/8 BACK
  • 98. Question: There are 6 short pieces of link chain, each having 4 links. It takes 10 seconds to cut a link and 25 seconds to weld it back together. What is the shortest possible time to make the longest chain?Hint and answer
  • 99. Hints:Connecting 2 chains requires one cut and oneweld . Answer: Time to connect two chains = 1 cut + 1 weld = 10s + 25s To connect all chains together = 5 connections =5(10+25)s =5(35) = 175 BACK
  • 100. Question:Magic HexagonFind the magic constant and fill in the numbers so that every column or diagonal has the same sum.Hint and answer
  • 101. Hints: Use the sum of the column of numbers given tofind the target total for each column or diagonalAnswer: BACK
  • 102. Question: An artist draws a picture of a house with a rose bush in front. In his picture the rose bush is 1.5cm high and the house is 7.5cm high. In reality the rose bush is .75 meters high. How tall is the house (in meters)?Hint and answer
  • 103. Hints:1) Convert meters to centimeters2) Find the artists scale, as indicated by the actual size of the rosebush compared to the size of the artists drawingAnswer: Let x = artists scale1) Convert meters (m) to centimeters (cm)In reality, rose bush = .75m*100 cm/m = 750 cm2) Solve for x 1.5x = 750 x = 750/1.5 x = 500 cm IF artists scale = 1 cm:500cm THEN In reality, house = 7.5cm * 500 cm = 3750 cm = 3.75 m BACK
  • 104. Question:This picture shows a triangle in which 3 lines are drawn to one or the other of the opposing sides from each of two vertices. This divides the triangle into 16 no overlapping sections.If 4 lines are drawn in the same way, how many no overlapping sections will the triangle have?Hint and answer
  • 105. Hint: The three lines divide the two sides in 4 pieceseach. Look at how many sections there would be if fourlines were extended from each vertex. Answer: When 3 lines are extended from vertex, opposite side is divided into four sections When 3 lines are extended from two vertices: Number of non over lapping sections formed = 42 = 16If 4 lines are extended from vertex, opposite side is divided into five sectionsTherefore, when 4 lines are extended from two vertices: Number of non over lapping sections formed = 52 = 25 BACK
  • 106. Question: The sports commentator on the CFXU radio station summarized the points scored by the St. F. X. Basketball Team during this season as follows: "The SMU scored a total of 1729 points in the last season. This year St. F. X. scored of 1653 points. ST. F.X. received 38 percent of the points for the total season of all 4 teams. SMU finished in second place. Acadia received only 14 percent of the points and was beaten for third place by Dalhousie by 50 points." If there were only 4 teams in the season, how many points did each team receive?Hint and answer
  • 107. Hints: ST. F.X. scored 1653 points, which was 38 percent of thetotal points. Find total number of points for all 4 teams. Answer: Let x = total number of points for the season1653 points were scored by ST. F.X., but ST. F.X. had only 38 percent of the total points for all four teams.Solve for x: x= 1653/0.38 = 4350 pointsACADIA: 14% * 4350 = 609DALHOUSIE: Acadia + 50 = 609 + 50 = 659 SMU: 4350 - (1653 + 609 + 659) = 1429 BACK
  • 108. Question: Rachel and Stephanie earn $5.15/hour. Rachel works 13 hours each week and Stephanie works 20 hours per week. Stephanie does not get any paid vacation time. How long a vacation would Stephanie have to take to make the same amount of money as Rachel in one year?Hint and answer
  • 109. Hints:Look at Stephanies weekly salary to determine how many weeks shemust work to make the same amount of money as Rachel makes inone yearAnswer: Rachel: WEEKLY: $5.15/hr * 13 hrs/wk = $66.95/wkYEARLY: $66.95/wk * 52 weeks = $3481.40/yr Stephanie: WEEKLY: $5.15/hr * 20 hrs/wk = $103/wk YEARLY: $103 * 52 weeks = $5356/yrIF Stephanie and Rachel make the same amount of money in one year, THEN Stephanie must only work: ($3481.40/yr)/($103/wk) = 33.8 weeks Therefore, she must take 52 - 33.8 = 18.2 weeks/yr Unpaid Vacation Time BACK
  • 110. Question:The Town of Antigonish has decided to put a paved path around Columbus Field. The path will be built so that the area of the park remains the same. If the path is to be 3m wide...a) What will be the perimeter of the path and the park? The dimensions of the park are 210m x 460m.b) What will be the area of the paved portion of the park?Hint and answer
  • 111. Hints:Draw a sketchAnswer: p = 2(6 + 210) + 2(6+460) = 432 + 932 Area of paved path = 2*3*466 + 2*3*210 = 4056 m2 BACK
  • 112. Question:  Joe buys a cup of coffee that costs $1.08. He pays with a two dollar coin.  If the cashier gives him 8 coins for his change, what could these coins be?Hint and answer
  • 113. Hints:There is more than one solution Answer: Amount of change Joe receives: $2.00 - $1.08 = $0.92 Two possible variations of coins received: (i) 3 quarters, 3 nickels, 2 pennies 3(.25) + 3(.05) + 2(.01) = .92 (ii) 2 quarters, 4 dimes, 2 pennies 2(.25) + 4(.10) + 2(0.01) = .92 BACK
  • 114. Question: Square ABCD has the centers of 4 equal circles as its vertices. Find the shaded area. Shawn bought a car for $5600.00. He sold it to Rachel for 5/6 the price he paid for it. Rachel sold it to Raelene for 1/5 less than she paid. Raelene sold it to Rick for 3/4 what she paid. What did Rick pay for the car?Hint and answer
  • 115. Hints:Length of sides of square equal 2 * radius of circle (circlesare equal)2) The square contains 4 quarters of equal circles Answer:Area of circle = pi * r2Side of square = 2 * r = 2r Area of square = (2r)2 = 4r2Area of shaded region = Area of square 4 * (1/4 area of each circle) = 4r2 - 4 * 1/4(pi * r2) = 4r2 - pi r2 = (4 - pi)r2 BACK
  • 116. Question: Points A and B on a map are 12km apart if you follow the path. A troop of boy scouts leaves point A at 11:00 a.m.. They are all carrying packs and travel 3km/hr until they reach point C at 12:45. If they want to reach point B by 2:00, how fast will they have to goHint and answer
  • 117. Hints: 1) Distance = Rate * Time2) Rate = Distance/TimeAnswer: Travel time from A to C = 12:45 -11:00 = 1 hr 45 min = 1.75 hr Distance travelled:D = Rate * Time = 3 km/hr * 1.75 hr = 5.25 km Distance remaining (from point C to B): = (12 - 5.25) km = 6.75km Time remaining = 2:00 - 12:45 = 1 hr 15 min = 1.25 hr Rate at which distance must be travelled: Rate = Distance/Time = 6.75 km / 1.25 hr = 5.4 km/hr BACK
  • 118. Question: Water conservation can be a big problem in some parts of the world. If a communitys water pump drips 3 drops every second and each drop is 1 1/3ml, how much water will be wasted in one year ?Hint and answer
  • 119. Hints:1) Look at how much water drips every second2) Calculate number of seconds in one year Answer: Water lost per second:3 * (1 1/3 mL) = 4mL Number of seconds in one year: 60s/min x 60 min/hr x 24hr/day x 365d/y = 31 536 000 s Water lost in one year = 4mL/s * 31 536 000 s = 126 144 000 Ml Convert to Litres:126 144 000mL * 1L/1000 mL = 126 144 litres BACK
  • 120. Question:  Shawn bought a car for P5600.00. He sold it to Rachel for 5/6 the price he paid for it. Rachel sold it to Raelene for 1/5 less than she paid. Raelene sold it to Rick for 3/4 what she paid.  What did Rick pay for the car?Hint and answer
  • 121. Hints:1) Calculate price each person paid for the car,working from Rachel to Raelene, to RickAnswer:PURCHASE PRICE:Rachel: 5/6 * P5600.00 = P4666.67Raelene: 4/5 * P4666.67 = P3733.33Rick: 3/4 * P3733.33 = P2800.00OR you can take a shortcut:Rick paid: P5600.00 (5/6)(4/5)(3/4) = P2800.00 BACK
  • 122.  Elmer Fudd decided to grow a garden so he could make salad. He wants to make it 10.1 m long and 4.2 m wide. However, in order to avoid Bugs Bunny from entering his garden he must make a fence surrounding the garden. He decides to make the fence 11.2 m long and 5.0 m wide. What is the area between the fence and the garden?Hint and answer
  • 123. Hints:1) Find area for the garden.2) Remember area equals length multiplied by width.3) Find the area of the space surrounded by the fence.Answer:13.58 m2 BACK
  • 124.  Jenny bought 7 t-shirts, one for each of her seven brothers, for P9.95 each. The cashier charged her an additional P13.07 in sales tax. She left the store with a measely P7.28. How much money did Jenny start with?Hint and answer
  • 125. Hints:1) What is the total amount the shirts would cost without the sales tax?2) If there is an additional P13.07 sales tax how much did the cashier charge her in total?3) How much did Jenny start with?Answer: P90.00 BACK
  • 126.  a) What is the least fraction of a full turn you could turn this geoboard for the shape to look the same? b) Try making your own figure on the same geoboard with the same turn symmetry.Hint and answer
  • 127. Hints:1) How many times could you turn the board and the shape still looks the same?2) Try labelling the figure and turning your sheet of paper.3)One full turn is when 1 returns to its original position.Answer:1/4 turn. BACK
  • 128.  Jill was given 3 red candies, 2 blue candies and 2 yellow candies. Use several ratios to describe the candies Jill has.Hint and answer
  • 129. Answer:3 red : 2 blue5 red and blue :2 yellow3 red : 7 candy. BACK
  • 130. A number line from 0 to 2 is divided into seven equal segments. What fraction names point A? What fraction names point B?Hint and answer
  • 131. Hints:• 1) What fraction, with denominator 7 reduces to a value of 2?• Example:• 12/6 = 2 but we want ?/7 = 2• (What is ?)• 2) If the line is divided into 7 segments, what would each point be labelled 0, 1/7, ... , ?/7=2 ?• 3) Or should they be named 0, 2/7, 4/7, 6/7, ......14/7 ?• 4) What is the fraction of A and BAnswer: BACK
  • 132.  a) If you saved P2.00 on January 1, P4.00 on February 1, P6.00 on March 1, P8.00 on April 1, and so on, how much money would you save in one year?  b) If you saved P2.00 on January 1, P4.00 on February 1, P8.00 on March 1, P16.00 on April 1, and so on. How much money would you save in one year?Hint and answer
  • 133. Hints:• 1) Make a chart to help you along with the problem. January 2 February 4 March 6 April 8 May ? June ? July ? August ? September ? October ? November ? December ? 2) How would you find the total amount of money you saved?• 1) Do the same as in the last problem.Answer:• a) 2+4+6+8+10+12+14+14+18+20+22+24 = P156.00• b) P8190.00 BACK
  • 134.  What is the number you started with?Hint and answer
  • 135. Hints:1) What are the factors of 12?2) Can the other number be 3? Why or why not? The numbers cannot be 3 because the greatest common factor of both of the numbers is 6. (3 cannot have a factor).3) Can the other number be 6? Why or why not?Answer:(462 * 3) / 0.1 = 13860 - 13860 / 308 = 45 ? = 45 BACK
  • 136. A Drug Store parking lot has space for 1000 cars. 2/5 of the spaces are for compact cars. On Tuesday, there were 200 compact cars and some standard size cars in the parking lot. The parking lot was 3/4 full.  How many standard size cars were in the parking lot?Hint and answer
  • 137. Hints:1) The parking lot is 3/4 full, how many cars are in the parking lot?2) If 200 of these cars in the parking lot are compact cars, how many are standard sized cars?Answer: 750 - 200 = 500 standard sized cars. BACK
  • 138.  How many triangles are in this figure?Hint and answer
  • 139. Hints:1) Count all the triangles you can see. 2) Some triangles are formed from smaller triangles.Answer: 12+6+2+6+1+6+2+2 = 37 BACK
  • 140. • Can you solve this magic square?• Put the remaining numbers from 0 to 15 in the 16 small squares. The sum of the four numbers in each row, column and two diagonals must be 30.• 15 | | | 12 ----+----+----+---- | 10 | 9 | ----+----+----+---- | | |11 ----+----+----+---- 3| | | 0 Hint and answer
  • 141. Hints:1) Start with a block you know you can fill then find the rest of the sums.Answer: 15 | 1 | 2 | 12 ----+----+----+---- 4 | 10 | 9 | 7 ----+----+----+---- 8 | 6 | 5 | 11 ----+----+----+---- 3 | 13 | 14 | 0 BACK
  • 142. • Mary and Jason were making propellers for their wooden helicopters. Mary put a number on her propellor and noticed that when she turned the propellor she had the same number. • Jason was trying to think of a number that he could put on his that had the same rotational synmetry (looks the same turned upside down). What is the next larger number that has this property?Hint and answer
  • 143. Hints:1) What other numbers have this same property?2) 0, 1, 6, and 8, 9, have this property?3) What is be the next lower number?Answer: 6009 BACK
  • 144.  Farmer Tom put a square fence around his vegetable garden to keep the deer from eating his corn. One side was 10m in length. If the posts were placed 2m apart, how many posts did he use?Hint and answer
  • 145. Hints:1) How many posts on one side of the square fence?2) If there are 4 sides how many posts are there all together?3) Remember if you found your answer to be 20 that you have counted the corner posts more than once.Answer: 5 posts/10m 16 BACK
  • 146. Ammie passed around a basket of strawberries to the girls at her party. Before the party she ate 5 strawberries and gave a friend 3. Eight girls arrived at the party. The first girl took a strawberry, the second girl took 3 strawberries, the third girl took 5 strawberries and so on. After the last girl took her strawberries, the basket was empty. How many strawberries were in the basket at the beginning?Hint and answer
  • 147. Hints:1) How many more strawberries did the second girl take then the first?2) Make a chart and look for a pattern. Girl | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 -------------+---+---+---+---+---+---+---+--- number of | | | | | | | | strawberries |1|3|5| | | | | taken | | | | | | | | -------------+---+---+---+---+---+---+---+--- total number | | | | | | | | taken |1|4|9| | | | | | | | | | | | | -------------+---+---+---+---+---+---+---+---3) What was the TOTAL amount taken?Answer: 72 BACK
  • 148. A side of square B is four times the length of a side of square A. How many times greater is the area of square B than the area of square A?Hint and answer
  • 149. Hints:1) If the side of square A = 1cm, what is the length of side B?2) What are the areas of square A and B?3) How many times greater is the area of square B than the area of square A?Answer:Let side of square A = 1 cmLet the side of square B = 4cm Area square A = 1 cm2Area square B = 16 cm2The area of square B is 16 times greater than the area of square A. BACK
  • 150.  Shane the Snail started at the dot. What side will he be on when he has crawled 13/20 of the distance around the regular pentagon of equal sides?Hint and answer
  • 151. Hints: 1) If side A has a length of 2cm, then what is the perimeter of this pentagon? 2) If he has crawled 13/20 of the total distance (perimeter) then how far has he crawled? And what side would this have to be?Answer: Let one side of a pentagon = 2 cm Therefore, perimeter = 10cm*(13/20) = 6.5cm SIDE D BACK
  • 152.  The number of hours that were left in the day was one-third of the number of hours already passed. How many hours were left in the day?Hint and answer
  • 153. Hints:1) If there were 9 hours left in the day, what was 1/3 of the number of hours that had already passed? Are they equal?2) If there were 8 hours left in the day, what was 1/3 of the hours that already passed? Are they equal?3) Try different numbers to find the number of hours left in a day that equals one-third of the number of hours that had already passed.Answer:9 hours left = 1/3 (15) 6 hours left = 1/3 (18)9 is not equal to 5 6 hours = 6 hours6 hours were left in the day. BACK
  • 154. A rectangular kitchen table is three times as long as it is wide. If it were 3m shorter and 3 m wider it would be a square. What are the dimensions of the rectangular table?Hint and answer
  • 155. Hints:1) If the length is 4m, what is the width of the rectangular table?2) Is this table a square? Why or why not?3) Make a table to help you. Length of Width of Length of Width of Correct? Rectangle Rectangle Square Square Trial #1 3x4m=12m 4m 12m 3m=9m 4m+3m=7m NO Trial #2 3x2m=6m 2m 6m-3m=3m 2m+3m=5m NO Trial #3Answer: width: 3m ; length: 3*3 = 9 width + 3 = 6 = length - 3 => a square BACK
  • 156. What is the starting number (?) ?Hint and answer
  • 157. Hints:1) When you square a number, you multiply the number by itself.ex: 2x2=4 = 2^2 3x3=9 = 3^22) Reverse your steps. (Work backwards starting with the result of 50).Answer: 42 is the starting number. BACK
  • 158.  Derek started his car (automatic shift) drove 9 km and spent 3 minutes waiting at traffic lights. About how much gasoline did Dereks car use?  CHART GIVEN: AUTOMOBILE FUEL USAGE Starting .015 Liters Idling for 1 minute .047Litres Moving Manual Shift 30km 3.0 Litres Automatic Shift 27km 3.0 LitresHint and answer
  • 159. Hints:1) If he spent 3 minutes idling, how much fuel did he burn in this amount of time?2) If it takes him 3.0 liters to go 27 km, how many liters can he go for 9km?3.0L/27km x 9km = ??3) What is the total amount of gasoline Dereks car used?Answer:Starting 0.015 + 3(0.047L) + (3.0L/27km * 9km) = 1.156 Liters of fuel BACK
  • 160. Heres a question for you!!!  One of these things does not belong here, one of these things is not the same. Can you tell which cube?Hint and answer
  • 161. Hints:1) Look at the patters on the cubes carefully.2) If it helps, try making paper cubes with these symbols.Answer:The third cube from left. BACK
  • 162.  Two carpenters decided to design desks for students at the Junior High. The dimensions of the desk are as shown. How much wood would they need for 30 desks? (in cm2).Hint and answer
  • 163. Hints:1) What is the area of one desk?2) Find the area of each part and add all the areas to find the total area.3) If there are 30 desks, how much wood in square centimetres do they need?Answer:Area of rectangle = 70cm x 30cm = 2100cm2Triangles 2*(1/2 20cm x 30cm) = 600cm2 2100cm2 + 600cm2 = 2700cm230*(2700cm2) = 81000cm2 of wood BACK
  • 164.  Chatterbox made the following figures with a piece of wood, 12 nails and an elastic band. What is the area of the figure (in units2)? Explain your method:Hint and answer
  • 165. Hints:1) You can do this in many different ways. You can divide the figure into different shapes to actually find the area of the figure. Or you may want to try a different way.Answer:There are different methods a student may have in mind. But here is one: Build a square around the shape. It has an area of 4 units. Then substract the area of the two triangles.Area = 2 ½ BACK
  • 166.  Do these parallelograms have the same area? How do you know?Hint and answer
  • 167. Hints:1) How do you find the area of a parallelogram?Answer:Yes, since you multiply the base and height, its really the same numbers, so it doesnt matter which is the base and which is the height. BACK
  • 168. PROBLEM  Find the next 3 numbers in the following sequence. 2, 5, 11, 23, ____, _____, ______.Hint and answer
  • 169. Solution and Answer 1.Find the next 3 numbers in the following sequence. 2, 5, 11, 23, ____, _____, ______. Pattern : x 2 + 1 47, 95, 191 BACK
  • 170.  .If this pattern was formed to make a cube, what numbers would appear where the question marks are?Hint and answer
  • 171.  2. If this pattern was formed to make a cube, what numbers would appear where the question marks are? ?=1 ?=4 ?=2 BACK
  • 172.  The number of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points.Hint and answer
  • 173.  .Thenumber of line segments joining a set of points increases as the number of points increases. Find how many line segments there will be when there are 8 points; 10 points. 1 Points 2 3 4 5 ...... 8 9 n 0 4 Lines 1 3 6 10 ...... 28 36 n(n-1) 2 5 + + + + + + + ...... 2 3 4 5 7 8 9 BACK
  • 174.  For the hexagon with 42 dots, how many dots are there on each side?Hint and answer
  • 175.  Forthe hexagon with 42 dots, how many dots are there on each side? No. of dots 6 12 18 ...... 42 n (n 6)+ Dots per side 2 3 4 ...... 8 1 BACK
  • 176.  Look for a common element in each of the following. This is a RUMDA. This is a not RUMDA. This is a RUMDA. Is this a RUMDA (A)? This is a RUMDA. Is this a RUMDA (B)? This is a not RUMDA.Hint and answer
  • 177.  Look for a common element in each of the following. This is a RUMDA. This is a not RUMDA. This is a RUMDA. Is this a RUMDA (A)?YES This is a RUMDA. Is this a RUMDA (B)?NO This is a not RUMDA. BACK
  • 178.  If the figure on the left is continued, how many letters will be in the J row?  Which row will contain 27 letters?  A BBB CCCCC DDDDDDHint and answer
  • 179. Solution and AnswerLetter A B C D E ...... J K L M N GeneralNumeral 1 2 3 4 5 ...... 10 11 12 13 14 nOrderTotal No. 1 3 5 7 9 ...... 19 21 23 25 27 2n-1 BACK
  • 180.  The Adams family was going to buy a car for $5800. The car dealer offered the Adams family two options for buying the car. They could pay the full amount in cash, or they could pay $1000.00 down and $230.00 a month for 24 months on the installment plan. How much more would they pay for the car on the installment plan?Hint and answer
  • 181.  Hints: 1) Try and calculate the amount of money that they would have to pay for the installment plan. 2) Calculate the difference between the installment plan and the initial amount if they paid today. Answer: 1000.00 + 230.00 * 24 = $6520.00 6250.00 - 5800.00 = $720.00 more for the installment plan. BACK
  • 182.  Lisa Lilly was the best runner in the eighth grade. One day she ran 100m in 40 seconds, 200m in 1 minute and 10 seconds, and 200m over low hurdles in one and a half minutes. How many more seconds did it take her to run the 200m over low hurdles then it did to run the 200m dash?Hint and answer
  • 183.  Hints: 1) What information is important in this question? 2) How long did it take her to run 200m in seconds? Answer: To run the 200m: 1 min = 60s + 10s = 70s To run 200m with hurdles: 60s + 30s = 90s 90s - 70s = 20s longer. BACK
  • 184.  Three students have to write a make up test. Mark scored 24/60 on his first test and 32/40 on his make up test. Jake scored 35/70 on his first test and 54/60 on his makeup test. Marilyn scored 27/90 on her first test and 45/50 on her second test.  A) Which student improved the most and by what percentage?  B) If the teacher gives each student a final grade using 70% of the makeup test mark and 30% of the first test mark, what mark would each student receive? Who did the best overall?Hint and answer
  • 185. Hints:1) Make a chart of the percentages scored on each test for each student. As the following: PERCENTAGE FOR FIRST TEST PERCENTAGE FOR SECOND TEST DIFFERENCEMARKJAKEMARILYN2) If you forget how to do percent, heres a hint: divide the denominator into the numerator and multiply by 100%Part BHint:1) Try making another chart with percentages of each test. Like the following: 30% of first test 70% of second test SumFinal MarkMARKJAKEMARILYNAnswer: A) | PERCENTAGE PERCENTAGE | FOR FIRST TEST FOR SECOND TEST DIFFERENCE---------------+--------------------------------------------------------MARK | 40% 80% 40%JAKE | 50% 90% 40%MARILYN | 30% 90% 60%B) | 30% of 70% of Sum Final | first test second test Mark---------------+--------------------------------------------------------MARK | 12% 56% 68%JAKE | 15% 63% 78%MARILYN | 9% 63% 72%Jake did the best overall. BACK
  • 186.  George, Sam, Andrew and Brandon each had four dates to four different Parish Center Dances with four different girls, named Cher, Connie, Melissa and Kendra. On the second date, George dated Connie and Brandan dated Kendra. On the third date Andrew went out with Melissa and Sam went out with Connie. Melissa went out with George and Cher went out with Sam on the fourth date. What couples went out together on the first date if no pairs went out more than once?Hint and answer
  • 187. Hints: 1) Make a chart to help you use logical reasoningAnswer: Cher dated George. Brandan dated Melissa Connie dated Andrew Sam dated Kendra BACK
  • 188.  A large piece of construction paper is .01mm thick. It is cut in half and one piece is placed on the other to make a pile. These are cut in half and all four pieces are placed in a pile. These four are cut in half and placed in a pile, and the process is continued. After the pieces have been cut and piled for the tenth time, what is the height of the pile in cm.Hint and answer
  • 189. Solution and Answer Hints:1) Try to draw a sketch of how many sheets are piled as the pile is cut each time.2) Now try to find a pattern in the numbers.3) How many sheets will you have after the sheets are cut and piled 10 times.4) How many cm high is this pile. Dont forget to change your mm to cm. Answer: 1 cut ---> 2 sheets 2 cuts---> 4 sheets 3 cuts---> 8 sheets 4 cuts---> 16 sheets ... 10 cuts--> 210 sheets 1024 (.01) = 10.24mm = 1.024 cm BACK
  • 190.  What is the sum of all the digits in the sequence 1, 2, 3, 4, 5, 6, 7,...99, 100?  NOTE: (Sum of the digits, not the numbers!)Hint and answer
  • 191. Hints:1) When all else fails, make a chart or a table. Start by writing the numbers in columns and rows.ex. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | | | | | | | | | | | | | | | | | | | |2) Now examine the digits in the rows (horizontal). What do you notice about digits? Try and find a pattern in the ones place.3) Carry on to find a pattern in the tens place.4) Dont forget about the number 100!!Answer: 10 (45) + 10 (45) + 1 = 901 1 + 10 * (the sum of the digits 1 to 9) + 10 * (the sum of the digits 1 to 9) = 901 BACK
  • 192.  Silvers Cleaners decided to raise the price of dry cleaning a sports coat from $4.00 to $5.00. The same percentage increase was applied to dry cleaning a jacket. The old cost of dry cleaning a jacket was $10.00. What is the new cost of dry cleaning a jacket?Hint and answer
  • 193.  Hints: 1) To find the percentage increase in the dry cleaning of a sports coat, set up an algebraic equation. 4 * x = 5.00 2) Now what is the price of the new cost of dry cleaning a jacket? Answer: Let x = percent increase 4.00 * x = 5.00 x = 5.00/4.00 * 100% = 125% 10.00 * 125% = $12.50 is the new cost of cleaning a jacket BACK
  • 194. A Christmas gift is tied with ribbon as shown. The bow requires 47cm of ribbon. What is the total length of the ribbon in metres?Hint and answer
  • 195.  Hints: 1) How many faces / sides are on a cube. How long is the piece of ribbon on each side? Find the total length of the ribbon on the sides. 2) Now the top and the bottom look like: What is the total length of the ribbon for the top and bottom? 3) Find the total length of all the ribbon in meters. Answer: On 4 sides 20cm of ribbon each = 80cm on the top and bottom. .5 * 10cm = 25cm 2 * 25cm = 50cm Total amount of ribbon 47cm + 50 cm + 80cm = 177cm = 1.77m BACK
  • 196.  Fourstrips of paneling 40 cm long and 4cm wide are arranged to form a square. What is the area of the inner square in cm2?Hint and answer
  • 197.  Hints: 1) Draw and label the diagram with the dimensions given. 2) Now find the inner dimensions of the paneling and find the area. Answer: 362 = 1296 cm2 BACK
  • 198.  In the following diagram of the front view of the Great Pyramid, the measure of the angle PRQ is 120 degrees, and the measure of the angle PST is 110 degrees. What is the measure of the angle RPS in degrees?Hint and answer
  • 199.  Hints: 1) Do you remember how many degrees there are in a triangle or a straight line? 2) There are 180 degrees in a triangle. That is the sum of the angles in a triangle is 180 degrees. A straight line is 180 degrees. 3) Say your diagram was as the following: ? = 180 degrees - 150 degrees ? = 30 degrees 4) Solve the problem!!! Answer: 180 degrees - 120 degrees = 60 degrees 180 degrees - 110 degrees = 70 degrees 60 degrees + 70 degrees = 130 degrees 180 degrees - 130 degrees = 50 degrees BACK
  • 200.  Mr. MacDonald recorded the test marks for his eighth grade class of 25 students. He used the marks recorded to calculate the average to be 72. Sandras mark of 86 was incorrectly marked as 36. What was the correct average for the test?Hint and answer
  • 201.  Hints:1) What does Mr. MacDonald have to do to find the average mark of his class?2) Average means the sum of the test marks divided by the number of students. So, what was the sum of all the tests?3) After you have the sum of all the tests you can find the correct average by correcting Mr. MacDonalds sum and finding the correct average. Answer: x / 25 = 72 x = 1800 = the sum of all the grades 1800 - 36 + 86 = 1850 1800 / 25 = 74% BACK
  • 202.  Chip said to Dale "If you give me one acorn, then we will have an equal number of acorns." Dale replied with delight "If you give me one acorn, then I will have double the number you have!" What was the total number of acorns they had in their tree? How many did Chip have and how many did Dale have?Hint and answer
  • 203.  Hints:1) Try different numbers that will satisfy the conditions given in the number.2) The sum of the numbers of acorns is twice six. Find out the how many Chip had and Dale had. Answer: Let C = # of acorns Chip had and D = # acorns Dale had. Then C + 1 = D - 1 ; D=! = 2(C-1). Solve to get C = 5 and D = 7. BACK
  • 204.  Bart Simpson decided to make a graph of his weekly earning of $120.00 from his paper route. To make the size of each sector proportional to the amount distributed what does the angle x in degrees have to be?Hint and answer
  • 205.  Hints:1) One way to overcome this problem is to think of percentages. What is the percent of $15 out of the total $120 earnings?2) Now we know what percent of his total earnings is. How many degrees are in a circle?3) The percent of money he spends on music is how many degrees in the circle? Answer: 45 degrees Percentages: $15/$120 *100% = 12.5% 360 degrees * 12.5% = 45 degrees BACK
  • 206.  Jane was walking the long way home from school. She started walking East. She walked 3 km East when she met a dog. She ran back to the school and decided to take the alternative route. So she walked North 4 km to her home. If she had walked straight home from where she met the dog, how far would it have been to her home?Hint and answer
  • 207.  Hints:1) Show diagram.2) Do you remember how to find the missing side of a right triangle?3) The Pythagorean theorem says, the hypotenuse, which is the longest side opposite the right angle, is equal to the square root of the sums of the squares of the other two sides.Z 2 = X2 + Y24) How many additional meters would she have to walk? Answer: 42 + 33 = ?2 25 = ?2 5km = ? 3km + 5km = 8km She would have to walk an additional 4 kilometers to get home from where she met the dog. BACK
  • 208.  The Gilliss house has a pool with the shape as shown. They want to make a cover for it for the harsh winter. How much to the nearest cent are they going to have to spend on material if it costs $5.00/m2.Hint and answer
  • 209. 1) You must find the total area of the pool.2) The pool can be divided into 3 different shapes.3) The area of a circle is A = Pi * r24) Find the total amount of money given that it costs $5.00 per meter squared.Answer: Areas: semi circle: area = Pi * radius squared = 1/2 Pi * r2 = 1/2 Pi (2m)2 = 1/2 Pi (4m,sup>2) = 2Pi m 2 triangle : area = 1/2 base * height = 1/2 (3m)(4m) = 6 m2 rectangle : area = (4m)(6m) = 24 m2 Total area = 24 + 2Pi + 6 = 36.28 m2. Cost = $5.00/m * 36.28 m,sup>2 = $181.42 BACK
  • 210.  Batman must solve the following problem to escape the Riddler. The mid- points of the sides of a square are joined as shown. A fraction of the original square is shaded. What is the fraction? Can you help him?Hint and answer
  • 211.  Hints:1) Divide the square into 4 equal parts. Can you see the answer? Answer: 1/4 BACK
  • 212.  Matthew is at a zoo. He takes a picture of a one-metre snake beside a brick wall. When he developed his pictures, the one-metre snake is 2cm long and the wall is 4.5cm high. What was the actual height of the brick wall in cm.Hint and answer
  • 213. Hints:1) If the snake is one meter long in real life and 2cm long in the picture, how high is the building if it is 4.5cm long in the picture.2) The easiest way to do this is to set up a ratio like: 100 x ---- = --- 2cm 4.5cm Solve for x, which is the height of the building.Answer: The snake is one meter long. 100/2 = x/4.5 x = 450/2 = 225cm high BACK
  • 214.  Joes rich uncle gave him a looney on his first birthday. On each birthday after that he doubled his previous gift. By the day after Joes eight birthday, what was the total amount that his uncle had given him?Hint and answer
  • 215. Hints:1) Make a chart-> 1st birthday $1 2nd birthday $2 3rd birthday $4 | |2) How much did he get in total?Answer: 1st birthday -> $1 2nd birthday -> $2 3rd birthday -> $4 $8 $16 $32 $64 $128 ------ $255 BACK
  • 216.  Ms. Smith, Ms. Gracia, and Ms. OLeary all teach at St. Andrew Junior High School. One of the women is a mathematics teacher, one an art teacher and one science teacher. The art teacher , an only child, has taught the least number of years. Ms. Garcia, who married Ms. Smiths brother, has taught more years than the mathematics teacher. Name the subject each woman teaches.Hint and answer
  • 217. Hints:1) Try to limit the amount of possibilities for each teacher.Example: Ms. Garcia cant teach art because she has taught more years than the mathematics teacher, and the art teacher has taught the least number of years.Answer: Mathematics Science Art | | | Ms. Smith Ms. Gracia Ms. OLeary BACK
  • 218.  Jim has three times as many comic books as Charles. Charles has two- thirds as many comic books as Bob. Bob has 27 comic books. How many comic books does Jim have.Hint and answer
  • 219. Hints:1) The best way to approach this problem is to work backwards. Try starting with statements: If Bob has 27 comic books and Charles has 2/3 as many, how many does Charles have?2) Jim has 3 times as many as Charles. So how many comic books does Jim have?3) If you need help in setting up equations, heres a start: 2/3 * # of Bobs comics = # of Charles comics =>Now do the same thing for Jim: 3 * # of Charles comics = # of Jims comicsAnswer: 2/3 * 27 = # of Charles comics = 18 Jim has 3 * 18 = 54 comic books BACK
  • 220.  FriendlysClothing Store bought handkerchiefs, six for $10, and sold them 4 for $10. They made $60 profit. How many handkerchiefs did they sell?Hint and answer
  • 221. Hints:1) First try and calculate how much Friendlys paid for each handkerchief when they bought them and how much a customer paid for each handkerchief. You can set up algebraic expressions to help you.6p = $10 and 4s = $10p = price of hamdkerchiefs and s = selling price of handkerchief-> Find p and s2) Now how can we tackle how many handkerchiefs they sold if the store made $60.00? One way to start is to set up an algebraic expressions that will solve for the number of handkerchiefs. If the store pays $10/6 for a handkerchief and sells it for $2.50 then how many should it sell make $60.00?(s-p)*x = $60.00-> Solve this algebraic equation for x, where x is the number of handkerchiefs.Answer: 6 for $10 4 for $10.00 1 for $10/6 1 for $2.50 x$2.50 - x$10/6 = $60.00 .83x = $60.00 x = 72 handkerchiefs. BACK
  • 222.  You, in your new red Porsche, decide to make a 160km trip to Carolina Beach, travelling at 80km/hr. You make the return trip travelling at a rate of 48km/hr. What was your average speed for the entire trip?Hint and answer
  • 223. Hints:1) In order to find the average speed, you must find the tthe total time it took you to travel to and from Carolina beach.2) Remember: Rate = distance/time3) The average speed is the total distance divided by the total time.Answer: How many hours in total does it take you? 160km/80km/hr = 2hr 160km/48km/hr = 3.33hr Average speed = (160 + 16)0/(2 + 3.33) = 60km/hr BACK
  • 224.  Who am I???  The names of my mother, my father, my brother, my sister and me in no particular order are Sandy, Sharon, Pat, Jennifer and Connie  Pat is younger than I am.  I am older than Connie.  Sharon is younger than Jennifer.Hint and answer
  • 225. Hints:1) This is a reasoning problem. Use the clues to figure out the problem.Answer:· -You must be a girl,· -Your brother Pat is younger than you,· -Connie is a younger sister,· -Jennifer must be the mother,· -You are Sharon. BACK
  • 226.  The points A, B, C, D, and E are located on a straight line in order.  The distance from A to E is 20cm.  The distance from A to D is 15cm.  The distance from B to E is 10cm.  C is halfway between B and D.  What is the distance from B to C?Hint and answer
  • 227. Hints:1) What is the distance from D to E?2) What is the distance from B to D?3) What is the distance from D to C?Answer: DE = 5cm BE = 10cm BC = 2.5cm BACK
  • 228.  Bob is reading a 445 page book. He has already read 157 pages. If he reads 24 pages a day, how long will it take him to finish the book? b) Bob read 157 pages of a 445 page book. He finished the rest in 9 days. How many pages did he average each day while completing the book?Hint and answer
  • 229. Hints:1) How many pages are in the book?2) How many pages has Bob read?3) How fast does he read?4) How many page does Bob have left to read?5) If Bob had 48 pages left to read, how many days would it take?6) How should you determine the number of days it will take to read 288 pages?b)Hints:1) Try using what you learned in part a to solve b.Answer:a) 445 - 157 = 288 pages left 288/24 = 12 It will take twelve days to finish the book.b) 288/9 = 32 pages a day BACK
  • 230.  Pioneer Video is giving away a free movie to anyone who can solve this puzzle. Place the numbers one to nine in the squares so that none of the rows, columns or diagonals have the same sum.  | |  ---+---+---  | |  ---+---+---  | |  Olivia won a free movie, what was her solution?Solution and answer
  • 231. Solution and Answer Hints:1) This is a trial and error problem. You must first try one set and then add up the rows, columns, and diagonals. If it works youve found an answer. Answer: 2|7|3 ----------- 4|6|9 ----------- 1|8|5 6|1|2 ----------- 4|5|7 ----------- 3|9|8 1|3|5 ----------- 2|4|6 ----------- 7|8|9 BACK
  • 232.  Homer Simpson entered a pie eating contest at the country fair. Homer was determined to win and went into training for 6 days. Each day he ate 4 more pies than the day before. Homer ate 150 pies while in training. How many pies did he eat each day?Solution and answer
  • 233. Solution and AnswerHints:1) Make a guess then check your guess!2) If Homer ate one pie the first day how many would he eat the second day?3) If he ate 10 pies on the first day, how many would he have eaten all together at the end of the 6 days?4) Would guessing that Homer ate 20 pies on the first day be a good guess?5) Try another number!Answer: 1st -> 15 2nd -> 19 3rd -> 23 4th -> 27 5th -> 31 6th -> 35 ----------- 150 pies BACK
  • 234.  Belgium Cheese costs $1.70 for 1/2 kilograms. How much will 2 and 1/2 kilograms of cheese cost?Solution and answer
  • 235. Hints:1) Set up a proportional equation2) $1.70/ 1/2 kilogram = x/2.5 kilogramsSolve for xAnswer: $1.70/.5 = x/ 2.5 .5x = 4.25/.5 x = $8.50 BACK
  • 236.  The Canadian record for the most consecutive sit-ups is 17,000 in 7 hours and 27 minutes.  At a rate of 40 sit-ups per minute, how many hours and minutes would it take to tie the record. Is this rate better than the Canadian record?Solution and answer
  • 237. Hints:1) How many sit-ups would you have to do to tie the record?2) If you can do 40 sit-ups per minute, how many minutes does it take to do 17,000?3) To answer the secnd part, what is the rate of sit-ups/minute of the Canadian record?Whose rate is better?Answer: 17000/7*60 + 27 = 38.03 sit-ups/min -> Record 17000/40 = 425 minutes = 7 hours and 5 minutes Your rate is better!! BACK
  • 238.  On an algebra test, I had seven times as many correct answers as incorrect ones. There were 120 items on the test, how many did I get right?Solution and answer
  • 239. Solution and AnswerHints:1) One way to approach this problem is with algebraic expressions. Let x = # of incorrect answers. What does the number of correct answers equal in terms of x?2) The number of items on the test equals the number of incorrect answers + the number of incorrect answers.Answers: x = # of incorrect answers 7x = # of correct answers 120 = 8x x = 15 incorrect 7*15 = 105 correct BACK
  • 240.  IfI pile grapefruit in a pyramid with 1 grapefruit in the first layer, 4 in the second layer (from the top), 9 in the third layer, and 16 in the fourth layer, how many grapefruit will I need to make a pile with 10 layers?Solution and answer
  • 241. Solution and AnswerHints:1) Is there a pattern in piling the grapefruit?2) Make a chart and find the sum. 1st 1 2nd 4 3rd 9 | | | |37)Answer: 1 -> 4 2 -> 9 3 -> 16 4 -> 25 5 -> 36 6 -> 49 7 -> 64 8 -> 81 9 -> 100 ---------------- 385 grapefruit BACK
  • 242.  Big-Bird wants to make a picture frame for his picture of Elmo. He is given the piece of plywood shown. He wants to make it in a shape (the shaded area). In order to do so, he must connect all the mid-points of the sides of a rectangle. What is the area of the piece of wood he will be using for the picture frame? What is the perimeter of the inside of frame?Solution and answer
  • 243. Hints:1) Try to decide how you could break up the figure and find the area.2) How would you find the perimeter? You must know the length of the sides.3) HINT!!! Divide the figure by connecting the midpoints of each side by a line. Now do youAnswer: x squared = 22 + 1.52 Perimeter = 4(2.5) = 10cm x = 2.5 Area of a triangle = 1/2*bh = .5 * 2 * 1.5 = 1.5 Area = 4(1.5) = 6 cm2 BACK
  • 244.  Whats the number Im thinking of? It is greater than 44 squared and less than 45 squared. 5 squared is one of its factors, and it is a multiple of 13.Solution and answer
  • 245. Hints:1) This is a trial and error problem. Answering these questions will help you:· a) What is the value of 44 squared?· b) What is the value of 45 squared· c) What is a factor? d) What does a mulitple mean? <- CHECK!!!!Answer: 2025 > x > 1936 1950 = 13 * 150 BACK
  • 246. A book exhibition was held for four days in a school. Number of tickets sold on first, second, third and fourth day were 1094, 1812, 2050 and 2751 respectively. Find the total number of tickets sold for the exhibitionSolution and answer
  • 247.  Number of tickets sold on the first day = 1094 Number of tickets sold on the second day = 1812 Number of tickets sold on the third day = 2050 Number of tickets sold on the fourth day = 2751 Total number of tickets sold = 1094 + 1812 + 2050 + 2751 = 7707 Hence total number of tickets sold = 7707 Ans BACK
  • 248.  Solve: (-7) - 8 - (-25)Solution and answer
  • 249.  (-7)- 8 - (-25) = -7 - 8 + 25Collecting & Solving like terms = -15 + 25 = 10 Ans BACK
  • 250.  Find cost of fencing a rectangular park whose length is 250 m, breadth = 175 m at P12 per meter.Solution and answer
  • 251. Length of rectangular park = 250 mBreadth of rectangular park = 175 mPerimeter of park = 2 (l + b) = 2 (250 m + 175 m) = 2 (425 m)Thus, perimeter of park = 850 m Cost of fencing 1 m = P 12 Cost of fencing 850 m = P 12 x 850 = P 10200 Ans BACK
  • 252.  The cost of 4 dozen bananas is Rs. 60. How many bananas can be purchased for Rs. 12.50 ?Solution and answer
  • 253.  Number of bananas bought for Rs. 60 = 4 dozen = 4 x 12 = 48 Number of bananas bought for Re. 1 = Number of bananas bought for Rs.12.50= x 12.50 = 10So, number of bananas bought for Rs. 12.50 = 10 Ans BACK
  • 254.  Aneesh made 42 runs in 6 overs. Anoop made 63 runs in 7 overs. Who made more runs in 1 over ?Solution and answer
  • 255. Aneesh made 42 runs in 6 overs. So, number of runs made in 1 over = = 7Anoop made 63 runs in 7 overs So, number of runs made in 1 over = = 9So, Anoop made more runs in 1 over BACK
  • 256.  The Band Committee of 100 people wishes to set up a telephone call system. The initial contact person calls three other people, each of whom call three others and so on, until all the people in the Band Committee have been contacted. What is the maximum number of people they need to make the calls.Solution and answer
  • 257. Hints:1) Try and draw a flow chart to explain how the telephone system works.2) How many people have to do the calling in order for 100 people to be called?ANSWER: 27 + 27 + 6 + 6 = 66 BACK
  • 258.  Mark and Fred had some money in the ratio 6:1. Mark gave half of his money to Fred. Find the ratio of the amount of money Mark had left to the amount of money Fred had in the end.Hint and answer
  • 259. AfterThe ratio of the amount of money Mark had left to the amount of money Fred had inthe end is 3:4. BACK
  • 260. • Carol puts some green and red unit cubes in a box. The ratio of the number of green cubes to the number of red cubes is 2:1. She adds 12 more red cubes in the box and the ratio becomes 4:5. • a) How many green cubes are there in the box? • b) How many red cubes does Carol have in the end?Hint and answer
  • 261. AfterFrom the model, we see that: a) 3 units = 12 cubes 1 unit = 12 ÷3 = 4 cubes 4 units = 4 × 4 = 16 cubesThere are 16 green cubes in the box. b) 5 units = 5 × 4 = 20 cubesCarol has 20 red cubes in the end.BACK
  • 262.  The weight of 25 bags of rice is 650 kg. Find the weight of hundred bags of rice?Hint and answer
  • 263.  since the weight of 25 bags of rice is 650kg.Then the weight of 1 bag of rice is 650 ÷ 25= 26kg Then weight of 100 bags of rice is 26 x 100= 2600 kg ANSWER2600 kg BACK
  • 264.  FindHCF of 136, 170 and 255 by division methodHint and answer
  • 265.  First we find the HCF of 136 and 170 136)170(1 136 34 HCF of 136 and 170 = 34 Now we find the HCF of 34 and 255 34)255(7 238 17)34(2 34 0 HCF of 34 and 255 =17 Hence HCF of 136,170 and 255 = 17 Find the LCM of 20, 30 and 50 by division method: 2] 20, 30, 50 5] 10, 15, 25 2, 3, 5 LCM = 2x 5x 2x 3x 5 = 300 BACK
  • 266.  Ken wants to make a half circle with a diameter of 5 cm, using a metal wire. How long is the wire he needs? What is the area of the half circle? Use pi = 3.14Hint and answer
  • 267.  Length of the wire = (5 x 3.14) ÷ 2 + 5 = 12.85 cm Area = (5/2)2 x 3.14 ÷ 2 = 9.81 cm2Answer 9.81 cm2 BACK
  • 268. A satellite orbits the earth at a height of 343 kilometers. If it makes 8 revolutions around the earth, how many kilometers does it travel? Earths diameter is 6371 kilometers. Use pi = 3.14Hint and answer
  • 269.  The diameter of the circle that the satellite travels is 6371 + 2 x 343 = 7057 kilometers; The answer is: 7057 x 3.14 x 8 = 177271.84 kilometers Answer 177271.84 kilometers BACK
  • 270.  Jane went to the store to buy some clothes. There was one sweater with an original price of $40. It was 15% off that day. Jane bought that sweater. (a) What was the cost of the sweater? If Jane pays 8% sales tax, how much did Jane pay for the sweater including the sales tax?Hint and answer
  • 271.  40x 15% = $6, $40 -$6 = $34 is the cost of the sweater. Sales tax is $34 x 8% = $2.72; Therefore Jane paid $34 + $2.72 = $36.72Answera) $34, b) $36.72 BACK
  • 272.  Charlie Joe Purple has been taking math tests. The average score of his first 3 test is 95 points. The average score of his next 2 test is 90 points. What is the Charlies average score of all 5 tests?Hint and answer
  • 273. (95 x 3 + 90 x 2) ÷ 5 = 93Answer93 BACK
  • 274.  5thgrade classes at Franklin Elementary completed a final science test. The average score of the female students is 82, and the average score of the male students is 79. There are 42 girls, and 38 boys in the 5th grade. What is the average test score of the entire 5th grade?Hint and answer
  • 275. Find the total score from all the students: 82 x 42 + 79 x 38 = 6446 Divide the total score by the total number of students: 42 + 38 = 80 (82 x 42 + 79 x 38) ÷ (42 + 38) = 6446 ÷ 80 = 80.6 Answer 80.6 BACK
  • 276.  ABCD and MNOP are squares. M, N, O, and P are at mid point of the 4 sides of square ABCD. If MN is 8 inches, what is the area of square ABCD?Hint and answer
  • 277.  Draw lines PN and MO. You can see that area of square MNOP is half of the area of ABCD. The area of square MNOP is 8 x 8 = 64 square inches; Area of ABCD = 2 x 64 = 128 square inches Answer 128 square inches BACK
  • 278.  Smart multiplications a) 39 x 5 x 20 b) 25 x 125 x 32Hint and answer
  • 279.  (a) Rearrange the numbers to 39 x (5 x 20) = 39 x 100 = 3900 (b) Rearrange the numbers to 25 x 125 x 4 x 8 = 25 x 4 x 125 x 8 = 100 x 1000 = 100000 Answer BACK
  • 280.  The area of the rectangle is 224 square inches. The length of the rectangle is 14 inches. What is the perimeter of the rectangle?Hint and answer
  • 281. The other side of the rectangle is 224 ÷ 14 = 16. The perimeter = 14 x 2 + 16 x 2 = 60 inchesAnswer 60 inches BACK
  • 282.  Smart multiplications a) 125 x 88 b) 108 x 125Hint and answer
  • 283. a) Rearrange the numbers to 125 x (80 + 8) = 10000 + 1000 = 11000 b) Rearrange the numbers to (100 + 8) x 125 = 100 x 125 + 8 x 125 = 12500 + 1000 = 1350Answers a) 11000, b) 13500 BACK
  • 284. Calculate a) 36.12 x 7.8 b) 42.3 x 3.5Hint and answer
  • 285. Answer a) 281.736, b) 148.05 BACK
  • 286. Jerrys train has 4 cars of different colors, yellow, green, red and blue. How many different ways can Jerry arrange his train cars?Hint and answer
  • 287. 4 x 3 x 2 = 24Answer 24 BACK
  • 288. A basket has 15 apples, 8 oranges and 27 plums mixed randomly. If you close your eyes and grab a fruit from the basket, what is the probability of you getting an orange?Hint and answer
  • 289. The total number of fruits is 50. So theprobability of picking an orange is 8/50 or4/25.Answer 8/50=4/25 BACK
  • 290.  Nina has sweaters that are pink, blue, red, and gray. She has pants that are: khaki, black and blue. How many different combinations of sweaters and pants can she wear?Hint and answer
  • 291. 4 x 3 = 12Answer 12 BACK
  • 292. Use the signs “+”, “-” , “x” and/or ( ) to make the equation work. Find 2Hint and answer
  • 293. 1) 1 + 2 + 3 + 4 + 5 + 6 + 7 + (8 x 9) = 1002) (1 + 2) x 3 + (4 x 5) + 6 + (7 x 8) + 9 = 100Answer: 100 BACK
  • 294.  What is the surface area of the following structure made of 5 cubes glued together. The side of each cube is 1 inch? Only consider the surfaces that are exposed.Hint and answer
  • 295. Count the number of cube you can see systematically.Answer 22 square inches BACK
  • 296. • Method 1: Looking from front: 4; back: 4, Left: 3, right: 3, Top: 4, Bottom: 4; The number of cube surfaces are 4 x 2 + 3 x 2 + 4 x 2 = 22 square inches • Method 2: Surfaces by cube: The four visible cubes have 5 surfaces each. The cube in the back has 2 surfaces. The number of cube surfaces are 5 + 5 + 5 + 5 + 2 = 22 square inches • what are all the factors of 124?Hint and answer
  • 297. Answer 1, 2, 31, 62, 124 BACK
  • 298.  Since 124 is an even number, 2 is a factor. 124 ÷ 2 = 62 which is an even number, therefore 4 is a factor. 62 ÷ 2 = 31, therefore 31 is a factor. 31 is a prime number.  What three consecutive odd numbers have a product of 15525?Hint and answer
  • 299. Answer 23 x 25 x 27 = 15525 BACK
  • 300. Fill in the squares with single digits (1 to 9) so that the sum of the 4 numbers equals to 120.Hint and answer
  • 301. Start with the ones place. The sum is 0. Therefore the the sum of the 4 digits at the ones place needs to be 10 or 20. 1 + 2 + 3 + 4 = 10, or 1 + 3 + 7 + 9 = 20. The sum of the 3 digits on the tens place plus the carry over needs to be 10 or 11. Try them out and you will get the answers.AnswerThere are more answers. Here is oneexample BACK
  • 302.  Today is Saturday. What day of the week is it 200 days from today?Hint and answer
  • 303. There are 7 days in a week. 200 ÷ 7 = 28R4;Therefore, 200 days from today is WednesdayAnswer Wednesday BACK
  • 304.  A, B and C each represents a different number between 1 and 9. What do A, B and C represent in the following addition problem?Hint and answer
  • 305. Answer BACK
  • 306.  What is the surface area of the following structure made of 8 cubes glued together. The side of each cube is 1 inch. Only consider the surfaces that are exposed.Hint and answer
  • 307. Answer 32 square inches BACK
  • 308. Count the number of cube you can see systematically. Looking from front: 4; back: 4, Left: 7, right: 7, Top: 5, Bottom: 5; The number of cube surfaces are 4 x 2 + 7 x 2 + 5 x 2 = 32 square inches you have a blue coin and a yellow coin. Place them in the following squares so that the blue one is always 1 row above the yellow one. How many different ways are there to place them in this manner?Hint and answer
  • 309.  Blue one in the first row: 3, Blue one in the 2nd row: 3 x 5 = 15; Total = 3 + 15 = 18Answer 18 BACK
  • 310.  Find the sequence and fill in the blanks  (1 ,4, 8), (2, 8, 16), (3, 12, 24), (4, 16, 32), ... The 10th group is (__, __, __)Hint and answer
  • 311. Leading number sequence is 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 Middle number sequence is 4, 8, 12, 16, 20, 24, 28, 32, 36, 40 The ending number sequence is 8, 16, 24, 32, 40, 48, 56, 64, 72, 80Answer (10, 40, 80) BACK
  • 312. A farmer has 150 rabbits. There are 4 times as many female rabbits as male rabbits. How many male and female rabbits are there?Hint and answer
  • 313. • Solutions: You do not need algebra to solve this problem. Instead, use a graph shown to help solve the problem. Each line represents an unknown number of rabbits.• Male rabbits ___ Female rabbits ___ ___ ___ ___• There are totally 5 lines, which is equivalent to 150 rabbits. Therefore, each line represents 150 ÷ 5 = 30 rabbits; Male rabbits = 30 Female rabbits = 30 x 4 = 120Answer Male rabbits = 30 Female rabbits = 120 BACK
  • 314.  Annie, Betty and Corina went to the farm to pick apples. The total number of apples they picked were 120. Annie picked twice as many as Betty did, and Betty picked 3 times as many as Corina did. How many apples did they each pick?Hint and answer
  • 315.  You do not need algebra to solve this problem. Instead, use a graph shown to help solve the problem. Each yellow bar represents some number of apples. For example, the number of apples Corina picked is represented by 1 bar. Since Betty picked 3 times as many as Corina did; 3 yellow bars represents what she picked. The number Annie picked is represented by 6 yellow bars. There are totally 10 bars, which is equivalent to 120 apples. Therefore, each yellow bar is equivalent to 120 ÷ 10 = 12 apples. Therefore Annie picked 72 (= 12 x 6) apples, Betty picked 36 (= 12 x 3) apples, and Corina picked 12 apples.Answer Annie = 72 Betty = 32 Corina = 12 BACK
  • 316. What is in the ones place of the product below? 3 x 3 x 3 x 3 x 3 x 3........... to a total of thirty-four threeHint and answer
  • 317. SOLUTION 3 3x3=9 3 x 3 x 3 = 27 3 x 3 x 3 x 3 = 81 3 x 3 x 3 x 3 x 3 = AB3 ...........................Answer 9 BACK
  • 318.  Ling has some chickens and rabbits. There are 22 feet and 8 heads in all. How many chickens and rabbits does Ling have?Hint and answer
  • 319. First assume Ling has only chickens and no rabbits.8 chickens would have 16 feet. However, since there are 22 feet in all, there are 6 extra feet (22 - 16 = 6).Each rabbit has 2 additional feet compared with a chicken. Therefore, there has to be 3 (6 divided by 2) rabbits.ANSWERLing has 3 rabbits and 5 chickens. BACK
  • 320.  Rochelle took her final tests of several subjects. Her average score NOT including English is 88. Her average score including English is 90. Her English score is 98. How many subject tests did she take?Hint and answer
  • 321. The difference between the English score and the average of the other subject test scores is 98 - 88 = 10;The increase in average score when English is include is 90 – 88 = 2; The number of tests is (98 - 88) ÷ (90-88) = 10 ÷ 2= 5ANSWER5 subjects BACK
  • 322.  The length of AE is 80 millimeters. B is the midpoint of AD, C is the midpoint of BD, and D is the midpoint of CE. How long is line AB?Hint and answer
  • 323. Answer 40 millimeters BACK
  • 324.  The diameter of the circles is 2 cm. Calculate the area that is purpleHint and answer
  • 325. The purple area is the area of the square subtract the area of the 4 circles. The sides of the square is 4 cm.Therefore the purple area is 4 x 4 - 4 x (3.14 x 1 x 1) = 3.44 square cmANSWER3.44 square cm BACK
  • 326.  How many triangles are there?Hint and answer
  • 327. Answer 22 BACK
  • 328.  Arpan started to read a novel. He read 15 pages a day. After 6 days he had 3/8 of the pages left. How many pages are there in the book?Hint and answer
  • 329. Answer 144 pages BACK
  • 330.  Which fraction has a larger value? ORHint and answer
  • 331. • Answer is larger• Smart way to solve the problem: is greater than is smaller than BACK
  • 332. A half circle overlaps with a square. The diameter of the half circle is 12 inches. What is the area of the hatched parts?Hint and answer
  • 333. The 2 quarter circles are exactly the same. Therefore the hatched area is the same as the area of the square on the left, which is 6 x 6 = 36 square inches.Answer 36 square inches BACK
  • 334.  The weight of a box of chocolates is 2.2 pounds. After taking out 3/4 of the chocolates, the remaining chocolates and the box weigh 0.7 pounds. What is weight of the box, and the weight of the chocolates before any chocolates were taken out?Hint and answer
  • 335. Chocolates taken out = 2.2 - 0.7 = 1.5 lbs,which is 3/4 of all the chocolates.Therefore the total weight of thechocolates is 1.5 ÷ (3/4) = 2 pounds.ANSWER 0.2 POUNDSBACK
  • 336. A brand new movie just came to Golden Theater. The theater has a goal of selling 1500 tickets for this movie in the 1st week. The first 2 days it sold 30% of goal tickets. What is the average number of tickets the theater needs to sell in the next 5 days in order to meet the goal?Hint and answer
  • 337. The next 5 days sales needs to be 1500 x (100% - 30%) = 1050 tickets; Average daily sales = 1050 e 5 = 210 tickets Answer 210 tickets BACK
  • 338. If A Δ B = 1 + 2 +3 + 4 + ..... + (A x B) Example: 2 Δ 3 = 1 + 2 + 3 + 4 + 5 + (2 x 3) Calculate (4 Δ 5) - (2 Δ 3)Hint and answer
  • 339. (4 8 3) = 1 + 2 + 3 + 4 + ......+ 12 = 78 (2 8 3) = 1 + 2 + 3 + 4 + 5 + 6 = 21 78 -21 = 57ANSWER 57BACK
  • 340.  Gasoline price is $4.0 / gallon in August. The price increased by 10% in September, and dropped 5% in October. What the gasoline price in October?Hint and answer
  • 341. Price in September = $4.0 + $4.0 x 10% =$4.40Price in October = $4.40 - $4.40 x 5% =$4.18ANSWER $4.18
  • 342. Fill in the blanks with the same natural number to make the equation correct. 3_ x 4128 = 3264 x _3Hint and answer
  • 343. To make the ones digit on both sides to bethe same, i.e. 2, the unknown number canbe 4 or 9. However, 93 will make the rightside of the equation much larger than theleft side. Answer 4BACK
  • 344.  John went to the stores to buy Christmas presents for his kids. He spent 2 thirds of his money at a book store. He then spent 1 third of the remaining money at a craft store. At the end he had $8 left. How much money did he have at the beginning?Hint and answer
  • 345. Money spent at the craft store = 8 ÷ (1 - 1/3) = $12, which is 1/3 of all the money he had at the beginning; Therefore, 12 e (1/3) = $36 is what John had at the beginning of his shopping trip.Answer $36 BACK
  • 346.  Ming Lees birthday is on February 25th. If January 1st of 2009 is Thursday, which day of the week is Ming Lees birthday in the year 2009?Hint and answer
  • 347. There are 31 days in January. There are31 + 25 - 1 = 55 days from January 1st toFebruary 25th. There are 7 days in a week.55 ÷ 7 = 7R6;Therefore February 25th is on aWednesdayANSWERWednesdayBACK
  • 348.  You are given this graph of a triangle DEF and you are asked its area. What do you think it is?Hint and answer
  • 349. Hints:1) What is the formula for the area of a triangle?2) What is the length of the base? The length is the change in x !3) What is the height of the triangle? The height is the change in y!4) What is the area?ANSWER: a = 1/2bh b=8-1=7 a = 1/2(47) h=5-1=4 = 1/2(28) a = 14 Units2 BACK
  • 350.  Fillin the squares with single digits (1 to 9) so that the sum of the 4 numbers equals to 120.Hint and answer
  • 351.  Answer There are more answers. Here is one example: Start with the ones place. The sum is 0. Therefore the the sum of the 4 digits at the ones place needs to be 10 or 20. 1 + 2 + 3 + 4 = 10, or 1 + 3 + 7 + 9 = 20. The sum of the 3 digits on the tens place plus the carry over needs to be 10 or 11. Try them out and you will get the answers BACK
  • 352.  you have a blue coin and a yellow coin. Place them in the following squares so that the blue one is always 1 row above the yellow one. How many different ways are there to place them in this manner?Hint and answer
  • 353. Answer 18Blue one in the first row: 3, Blue one in the 2nd row: 3 x 5 = 15; Total = 3 + 15 = 18 BACK
  • 354.  Soma the dog runs along a railroad. A train that is 270 meters long passes her in 18 seconds. The speed of the train is 20 meters/second. What is Somas speed?Hint and answer
  • 355.  Solution: Lets call Somas speed S. 20 x 18 - S x 18 = 270 (the trains speed) Therefore Somas speed S = (20 x18 -270) e 18 = 10 meters/second Answer10 meters per second BACK
  • 356.  October 1st of 2008 is Wednesday. What day of the week is Christmas day, December 25th of Christmas of 2008?Hint and answer
  • 357. There are 31 + 30 + 25 - 1 = 85 days from January 1st to February 25th. There are 7 days in a week. 85 ÷ 7 = 12R1; Therefore December 25th is on a Thursday. Answer Thursday BACK
  • 358.  A rectangle prism is 8 cm long, 4 cm wide and 4 cm tall. a) How many 2 x 2 x 2 cm cubes can the prism be cut into? b) What is the total surface area of all the 2 x 2 x 2 cm cubes? c) What is the total volume of all the 2 x 2 x 2 cm cubes?Hint and answer
  • 359. a) 16, See the picture b) 1 cube has surface area of (2 x 2) x 6 = 24 square cm; 4 cubes have surface area of 24 x 16 = 384 square cm c) 4 x 4 x 2 = 32 cubic cm, (same as the volume of the original prism) BACK
  • 360.  There are 3 identical wooden blocks that are 50 inches long, 5 inches wide and 2 inches thick. If you glue them together, what is the largest and smallest outer surface area you can get?Hint and answer
  • 361. To get the smallest surface area, you need to glue the largest surfaces together, in this case 50 x 5 inch surfaces. Therefore, the smallest surface area is:To get the smallest surface area, you need to glue the largest surfaces together, in this case 50 x 5 inch surfaces. Therefore, the smallest surface area is: (50 x 8 + 8 x 5 + 50 x 5) x 2 = 1380 square inchAnswer largest = 3120 square inch, smallest = 1380 square inch BACK
  • 362.  A train is 300 meters long. A tunnel is 2900 meters long. The train travels at 600 meters/minute speed. How long is the time between the moment the front of the train enters the tunnel and the moment the end of the train exits the tunnel?Hint and answer
  • 363. The length the train needs to travel is 1100 +300 =2400 meters,Therefore, it takes 2400 ÷ 600 = 4 minutesfor the train to pass the tunnel.Answer 4 minutesBACK
  • 364.  Tims shoe store just stocked 104 pairs of new shoes. The ratio of black shoes and brown shoes is 5 to 3. How many pairs of black shoes and brown shoes did the store stock?Hint and answer
  • 365. The portion of black shoes is 5/(5 + 3) = 5/8 The portion of brown shoes is 3/(5 + 3) = 3/8 Black shoes = 104 x 5/8 = 65 pairs Brown shoes = 104 x 3/8 = 39 pairsAnswer Black shoes: 65 pairs Brown shoes: 39 pairsBACK
  • 366.  The square has an area of 100 square cm. What is the area of the circle?Hint and answer
  • 367. The diameter of the circle is the same as the sides of the square. Therefore the area of the circle is 3.14 x (10/2)2 = 78.5 square cmAnswer 78.5 square cmBACK
  • 368.  Four kids Aaron, Bessy, Carli and Dawn play with beads. They start with 200 beads in all. Aaron gave Bessy 26 beads, Bessy gave Carli 36 beads, Carli give Dawn 32 beads, and Dawn give Aaron 4 beads. They end up with the same number of beads. How many beads did each of them have at the beginningHint and answer
  • 369. Answer At the end they each had 50 beads. Aaron had 50 + 26 - 4 = 72 beads Bessy had 50 + 36 - 26 = 60 beads Carli had 50 + 32 - 36 = 46 beads Dawn had 50 + 4 - 32 = 22 beads BACK
  • 370.  Brady weighed 240 lbs. He lost 11 lbs the first week at the weight loss camp. He lost another 5 lbs the 2nd week. What percentage of his weight did he lose in these 2 weeks?Hint and answer
  • 371.  Total weight loss in 2 weeks = 11 + 5 = 16 lbs 16 ÷ 240 = 0.0667 = 6.67%Answer 6.67%BACK
  • 372.  Mrs. Jordan went to the stores to buy Christmas presents. She spent half of her money plus $7 at S-Mart. She then spent half of the remaining money plus $8 at Clever-Mart. At the end she had $35 left. How much money did Mrs. Jordan have at the beginning of her shopping trip?Hint and answer
  • 373. The money Mrs. Jordan had entering Cleaver-Mart = (35 + 8) x 2 = $86Answer $186BACK
  • 374. Hint and answer
  • 375. 1) If Elizabeth walks 2 km/h uphill, 6 km/h downhill, and 3 km/h on level ground, how long does she take to walk throughout each of the different levels?2) What is the total distance she walks at this rate?ANSWER:x - Distance of UphillY - Distance of DownhillZ - Distance Level GrounTotal walking time=6=(x/2+y/6+z/3)+(x/6+y/2+z/3)(This is used for her walking back --- uphill turns to down hill and downhill turns to uphill) 6(x/2+y/6+z/3+y/2+x/6+z/3)=36 36=4(x+y+z)===> x+y+z=36/4=9 ====> She walks 18km in total. BACK
  • 376. Joyce was decorating her store window for a going out of business sale. She wanted to make a figure that looks like the following. The shaded piece is made of a different material. How much material does she need in metres squared?Hint and answer
  • 377. 1) What is the area of a circle?2) How many circles or half circles can you see in the figure?3) Label your different circles. How would you be able to find the shaded area using the labelled circles?ANSWERArea of half Circle Area of radius 2-> A=Pi*r2 Pi/2 = Pi/2 =Pi (1)2 =Pi Area of little circle. A=Pi2 =Pi(.5)2 =Pi(.23) =Pi/4 Pi/4 * 1/2 = Pi/8 Pi/2 - Pi/8 = area of one 4Pi/8 - Pi/8 = 3Pi/8 3Pi/8 * 2 = 6Pi/8 = 3Pi/4 m2BACK
  • 378. In # 2 Mitch needed to find the material she would need for the shaded region. How much material would she need for the unshaded region in m2?Hint and answer
  • 379. You know the area of the shaded region. So how would you compute the area of the un shaded region?ANSWERArea of large circle A=Pi*r2 =Pi(1.5)2 =2.25Pi 2.25Pi - area shaded = 2.25Pi - .75(Pi)m2 = 3Pi/2m2 BACK
  • 380. George and Phil were playing with their fish tank again. They had a difficult time keeping their fish alive. The fish tank is 100cm long, 60 cm wide and 40 cm high. They tilted the tank, as shown, resting on a 60 cm edge, with the water level reaching the midpoint of the base. When they rest the tank down to a horizontal position, what is the depth of the water in cm?Hint and answer
  • 381. 1) What portion of the tank is filled?2) What is the volume of this portion?3) Does the volume change when it is turned horizontal?4) What is the depth?ANSWERVolume of the water = Volume of 1/2 of tank = 1/2 100cm * 40cm * 60cm = 120,000 1/2 (120,000) = 60,000 60,000 = 100 cm * 60 cm * d 10 cm = d BACK
  • 382. Alex, Fred and Thomas run at constant rates. In a race of 1,000m, Alex finished 200m ahead of Fred and 400m ahead of Thomas. When Fred finished, how far was he ahead of Thomas? (in m)Hint and answer
  • 383. 1) Let a variable t = time it takes Alex to run 1000m, Fred to run 800m and Thomas to run 600m. How fast do each of them run?2) If Fred runs another 200m to the fimish line, how long does it take him?3) How far does Thomas run in this time?4) How far behind is he?5) Setting up a table may help you. Maybe something like: Alex Fred Thomas ----------------------------------------------------------------Distance 1000m 800m 600mRate 1000/x 800/x 600/xTime ittakes to 0 200m*x/800 ?finish ANSWER>250m aheadLet x = time for Alex to finishLet t = time for Fred to finish Alex Fred Thomasdist at x 1000m 800m 600mSpeed 1000m/x 800m/x 600m/xFind the time it will take Fred to finish 200m/speed(Fred)=t 200m / 800m / x 200 * x / 800 = t x/4 = tHow far can Thomas go in that time(Fred was 200 ahead and will go antoher 200) t*speed(Thomas)600m/x * x/4 = 150m in that time 400 - 150 = 250m Thomas has 200m left to go. BACK
  • 384. If ABCD is a square and ABE is an equilateral triangle, then what is the measure of < BFC?Hint and answer
  • 385. 1) How many degrees are there in a triangle?2) There are 180 degrees in a triangle.3. How many right angles does a square have? (A right angle is an angle equal to 90 degrees)4) What is the measure of the angles in an equilateral triangle. Remember, all angles in an equilateral triangle are equal.5) Now label the different angles, what is the measure of < BFC?ANSWER Angle F = 105 degrees BACK
  • 386. An unusual die has six faces labelled 1,2,3,5,7 9. If two of these dice are rolled, and the numbers showing on the upper faces are added, what is the number of possible different sums?Hint and answer
  • 387. 1) Make a list of the different possible sums. Calculate the sums and cross out any sums that are replicates.2) Start with the number one. How many possible sums are there? Continue in this way. ANSWER 141+1, 1+2, 1+3, 1+5 1+7, 1+9, 2+3, 2+5, 2+7, 2+9, 3+9, 5+9, 7+9, 9+9. BACK
  • 388. The Quinn pool family decided to build a pool of the following shape. The sides of their 12 * 9 yard are trisected. What is the perimeter of the shaded pool?Hint and answer
  • 389. 1. What does it mean to be trisected?2.If each side is trisected, what is the lengths of each section?3.To find the lengths of the angled sides,4. You must use the pythagorean theorem. (The length of the hypoteneuse is equal to the square root of sum of the squares of the other two sides).ANSWER 42 + 32 = c2 16 + 9 = c2 25 = c2 c=5 BACK
  • 390. A classroom contained an equal number of boys and girls. Eight girls left to play hockey, leaving twice as many boys as girls in the classroom. What was the original number of students present?Hint and answer
  • 391. Draw a chart like the following to help you: Before After Correct? -----+---------+------+------+---------- | Girls | 10 | 2 |1 +---------+------+------+ No| Boys | 10 | 10 |-----+---------+------+------+---------- | Girls | 20 | 12 | 2 +---------+------+------+ No| Boys | 20 |(220 4) + (2 * 3) + (4 * 5) = 34 * | -----+---------+------+------+----------ANSWER:Let the number of girls or boys = x 2(x-8) = x 2x - 16 = x x=16 There are 2x students in the class, therefore there are 32 students. BACK
  • 392. Flora had an average of 56% on her first 7 exams. What would she have to make on her eighth exam to obtain an average of 60% on 8 exams?Hint and answer
  • 393. How would you find the average of 8 exams?But you already know the average of 7 exams,so what is the average of 8 exams?ANSWER Let x = the mark on the eighth exam. 56% = .56 (.56 * 7 + x)/8 = .60 3.92 + x = .60 * 8 3.92 + x = 4.80 x = 4.80-3.92 x = .88 = 88%BACK
  • 394. Coming out of the grocery store, Ebree has eight coins, of which none is a half-dollar, that add up to $1.45. Unfortunately, on the way home she loses one of them. If the chances of losing a quarter, dime or nickel are equal, which coin is most probably lost?Hint and answer
  • 395. 1. Could you have 4 quarters or 3 quarters and the rest of the coins are nickels and dimes?2. How many quarters could you have?Nickels? Dimes?3. Now that you know how many coins you can have, what are the probabilities of losing a quarter, a nickel or a dime?4. Which coin did she probably lose?ANSWERIf 4 or fewer are quarters and the rest dimes and nickels, it wouldnt bring the total to $1.45 with the 4 dimes or nickels. 5 are quarters -> $1.25 Other 3 dimes or nickels make up 20 cents.PROBABILITIES: Losing a quarter = 5/8 chances Losing a dime = 1/8 Losing a nickel = 2/8 = 1/4Greatest probability -> quarter <- Answer BACK
  • 396. Joe gives Nick and Tom as many peanuts as each already has. Then Nick gives Joe and Tom as many peanuts as each of them then has. Finally, Tom gives Nick and Joe as many peanuts as each has. If at the end each has sixteen peanuts, how many peanuts did each have at the beginning?Hint and answer
  • 397. Try setting up a table and work backwards to find out how many peanuts each of them started out with t | Joe | Nick | Tom ----------+----------+----------+---------- 4 | 16 | 16 | 16 3 | : | : | : 2 | : | : | : 1 | : | : | : ANSWERt Joe Nick Tom4 16 16 163 8 8 322 4 28 161 26 14 8 Joe - 26 Nick - 14 Tom - 8 Peanuts BACK
  • 398.  Stephanie wasnt very keen on Algebra. Her teacher gave her an Algebra problem and told Stephanie to solve it. She was having problems, can you help her?  3x + 7 = x2 + k = 7x + 15 What is the value of k?Hint and answer
  • 399. Hints:1) You have two equations. Try using one equation to find the value of x.2) Now use another equation to find the value of k. x2 + k = 7x + 15 or x2 + k = 3x + 7ANSWER: 3x + 7 = 7x + 15 -4x = 8 x = -2 (-2)2 + k = 7 (-2) + 15 4 + k = -14 + 15 k=1-4 k = -3 BACK
  • 400.  George Jefferson plans to drive from his home to Edmonton, a trip of 2200km. His car has a 24 gallon tank and gets 27km to the gallon. If he starts out with a full tank of gasoline, what is the fewest number of stops he will have to make for gasoline to complete his trip to Edmonton?Hint and answer
  • 401. Hints:1) How many kilometers can he go with a full tank of gas?2) How many times does he have stop?Answer: 2200km/27km = 27 * 24 = 648km for 24 gallons stop 1 after 648 km stop 2 after 1296 km stop 3 after 1944 km 3( 4 tanks of gas becasue he starts full) stops to complete his trip? BACK
  • 402. Question • Jill loves math but she hates this problem. Can you help her? The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by three, then all the results will be equal. What is the difference between the largest and the smallest of the original numbers?Hint and answer
  • 403. Hints:1) Let a, b, c and d be your four different numbers.2) Then a + 3 = b - 3 = ? = ? (Fill in the question marks) Let them all equal a variable x.3) What does x equal in terms of a, b, c and d?4) a + b + c + d =64 (In terms of x what does this equation look like?5) What does x equal? What do a, b, c and d equal?6) What is the difference between a and b?Answer: a + 3 = b - 3 = 3c = d/3 Let k equal the number all of them equal k=a+3 k=b-3 k = 3c k = d/3 a=k-3 b=k+3 c = k/3 d = 3k k - 3 + k + 3 + k/3 + 3k = 64 5k + k/3 = 64 16k/3 = 64 k = 12 a = 12 - 3 = 9 d = 3(12) = 36 36 - 9 = 27 BACK
  • 404. Question: • Regular pentagon ABCDE is enclosed in a circle. If the radius of the circle is 5 and each side AB = BC = CD = DE = EA = 5.88, find the area of the pentagon. • (In a 90 degree triangle, using pythagorean theorem c = square root of a2 + b2)Hint and answer
  • 405. Hints: 1) Use Pythagorean theorem: a2 + b2 = c2• 44) • h of each triangle =• Answer: square root of 5^2- AO = BO = CO = DO = EO 3^2 = = 5 Therefore, we have 5 isosceles 4.05 Aera = 5 triangles. The altitude (1/2)(4.05)(5.88) = of an isosceles 59.54 triangle intersects the side with which it makes the 90 degree angle.BACK
  • 406. Question: • Line AB is parallel to line CD • The semicircle AED has diameter AD of 6cm. What is the area of the trapezoid ABCD plus the semicircle AED?Hint and answer
  • 407. Hints: 1) Area of a trapezoid = 1/2 * h * sum of the top and bottom sides• Answer:Area of semicircle = 1/2 pi r2 r=3Area of Trapezoid = 1/2(AD)(AB+CD)Total Area = 1/2 pi (9) + 1/2(6)(12+8) = 74.137 cm2 BACK
  • 408. Question: • In the quadrilateral ABCD, angle A is 120 degrees, angle D is two thirds of angle C, and angle B is 90 degrees. Find angle C.Hint and answer
  • 409. Hints:1) The sum of the four angles of a quadrilateral is 360 degrees• Answer:• 360 degrees = 120 degrees + 90 degrees + C + (2/3 * C) 360 = 210 + 5/3 * C 150 = 5/3C 450 = 5C 450/5 = C 90 = CSubstitute: If C = 90 degrees, Then D = 2/3 * 90 = 60 degrees BACK
  • 410. Question: • Find the area of quadrilateral EFGH. • Given (HC)2 + (CG)2 = (HG)2Hint and answer
  • 411. Hints: 1) Use pythagorean theorem to find the length of one side of the square• Answer:• The four sides of EFGH are equal Find length of one side: To find HG: (HC)2 + (CG)2 = (HG)2 Square root (32 + 12) = HG Square root (10) = HG Since four sides are equal, Area of EFGH = (square root 10)2 = 10 BACK
  • 412. Question: • Two gear wheels A and B are in contact. One wheel (A) has 36 teeth. The other (B) has 24 teeth. How many times must the smaller wheel turn before the larger wheel completes a revolution?Hint and answer
  • 413. Hints: 1) Look at the ratio of the number of teeth in wheel B to wheel A• Answer: Each revolution of B meets 24 teeth of ATherefore, (36 - 24) = 12 teeth of wheel A are notmet with the first revolution of BSince 12/24 = 1/2 Wheel B must turn 1 1/2 times for every revolution of A BACK
  • 414. • Question: Two trees of height 20m and 30m have ropes running from the top of each tree to the bottom of the other tree. How high above the ground do the ropes intersect? • The trees are 40m apart.Hint and answer
  • 415. Hints:1) Use the sketch2) Use similar triangles• Answer:Triangle BAC similar Triangle EFCTriangle DCA similar Triangle EFATherefore, 30/h = 40/(40 - b) 20/h = 40/b 1200 - 30b = 40hSubstitute 1200 - 30b = 20b <-------------------- 40h = 20b1200 - 30b = 20b h = 1/2 b 1200 = 50b1200/50 = b Substitute 24m = b ---------------------> h = 1/2 (24m) h = 12 m BACK
  • 416. PROBLEM A motorcycle and a truck left a roadside diner at the same time. After travelling in the same direction for one and a quarter hours, the motorcycle had travelled 25km farther than the truck. If the average speed of the motorcycle was 60km/hour, find the average speed of the truck.Hint and answer
  • 417. HINTS1) Remember that rate = distance/time2) How far did the motorcycle travel?3) How far did the truck travel?ANSWER 60km/hr * 1.25hr = 75km = distance the motorcycle travelled 50km/1.25hr = 40km/hr The average speed of the truck is 40km/hr BACK
  • 418. PROBLEM • Similar rectangles are constructed on the sides of a right triangle as shown. Find their areas and a relationship among those areas. Have you seen a similar relationship?Hint and answer
  • 419. HINTS1) When you have found the areas of the rectangles, what do you notice?2) What is the sum of the smallest rectangles equal to?3) Can you see a relationship?ANSWER 19.5 * 26 = 507 7.5 * 10 = 75 18 * 24 = 432 432 + 75 = 507The sum of the areas of the rectangles on the legs equals the area of the rectangle on the hypoteneuse. Relates to the Pythagorean Theorem. BACK
  • 420. PROBLEM • Triangle PQR is equilateral. QR = 30 units, B is the midpoint of QA. QA is perpendicular to PR. What is the length of PB?Hint and answer
  • 421. HINTS1) What are the properties of an equilateral triangle?2) What is the length of AR?3) Using the Pythagorean Theorem, What is the length of QA? Therefore, what is the length of BA?4) Again, using the pythagorean theorem, what is the length of PB?ANSWER Pr = 30 units PB = 19.84 302 = 152 + x2 302 - 152 = x2 6751/2 = x 6751/2 / 2 = BA (6751/2 / 2)2 + 152 = 42 393.751/2 = 4 19.84 = 4 BACK
  • 422. PROBLEM • I have sold 2/3 of my pencils for $0.15 each. If I have 8 pencils left, how much money did I collect for the pencils I sold?Hint and answer
  • 423. HINTS1) If I sold 2/3 of my pencils, what fraction of my pencils do I have left?2) Let the total number of pencils be a variable x. Therefore how many pencils do I have? 3. How much money did I make?ANSWER1/3 * x = 8 x = 24 2/3 (24) = 16 * .15 = $2.40 BACK
  • 424. PROBLEM • The minute hand of a clock is 6cm long. To the nearest centimeter, how far does the tip of the minute hand move in 35 minutesHint and answer
  • 425. HINTS1) What is the circumference of the clock?2) How far would the hand travel in 30 minutes?3) How far would the hand travel in 5 minutes?4) Therefore, how far would the hand travel in 35 minutes?ANSWERC of Clock = 2Pi (6) = 12Pi (1/2)12Pi = 6Pi (1/12)12Pi = PiTherefore 6Pi + Pi = 7Pi cm BACK
  • 426. PROBLEM• The numerator of a certain fraction is 3 less than the denominator. If the numerator is tripled and the denominator is increased by 7, the value of the resulting fraction is 3/2. What was the original fraction? x = denominator x-3 = numeratorHint and answer
  • 427. HINTS1) If the denominator is x, then what is the numerator?2) If the numerator is tripled, what does it become?3) If the denominator is increased by 7, we know that it will become x + 7.4) Set up the algebraic equation, cross multiply and solve for x.5) Remember that x is your denominator, so what is the resulting fraction? ANSWER3(x-3)/x+7 = 3/2 2(3x-9) = 3(x+7) 6x - 18 = 3x+21 3x = 39 x = 13 10/13 BACK
  • 428. PROBLEM • Darryl ate 100 peanut butter cups in five days. Each day he ate six more than he ate the previous day. How many peanut butter cups did Darryl eat on the first day?Hint and answer
  • 429. HINTS1) If x is the amount of peanut butter cups he ate the first day, then how many did he eat the 2nd day?2) How many did he eat the 3rd day? 4th day? 5th day?3) Add the amount of cups he ate on all five days and equate it to 100 (which is the total amount). Solve for x.ANSWER100 in 5 days. x <- st day x+6 <- 2nd day x+12 <- 3rd day x+18 <- 4th day x+24 <- 5th day x + x+6 + x+12 + x+18 + x+24 = 100 5x + 60 = 100 5x = 40 x=8 1st day he ate 8 BACK
  • 430. PROBLEM What is the next term in the sequence? 2, 10, 202, ______.Hint and answer
  • 431. HINTS1) How would you get the number 10 from the number 2 or the number 202 from the number 10?2) If you square the first number and add two, do you get the correct sequence?3) What about if you square the first number and multiply by two?4) What are you missing? ANSWER22 * 2 + 2 = 10 102 * 2 + 2 = 202 2022 * 2 + 2 = 81610 BACK
  • 432. PROBLEM Solve the magic square: 42 | | 40 ----+----+---- | | ----+----+---- 38 | 43 | 36Hint and answer
  • 433. HINTS1) One of the properties of a magic square which you have learned or will learn this year is that the numbers in the square are consecutive.For example: 2 | 9 | 4 -----+-----+----- 7 | 5 | 3 have numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, -----+-----+----- 6 | 1 | 8have numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 36, 38, 39, 40, 41, 42, 43.3) What is the magic square sum? ANSWER 42 | 35 | 40 ----+----+---- 37 | 39 | 41 ----+----+---- 38 | 43 | 36 BACK
  • 434. PROBLEM • Lilly had a math project to do for her geometry class. Her teacher wrote, "A cuboctohedren is a polyhedron that can be formed by slicing a cube at the midpoints of its edges." Lilly had to find the surface area of the cuboctobedren formed by a cube having a side of length 4cm?Hint and answer
  • 435. HINTS ANSWER1) What is the surface area of the diamond facing Six Faces -> LENGTH OF SQUARE you? What is the length of one of its sides? A = 81/2 * 81/2 = 8 (HINT: use the pythagorean theorem). Therefore 6 * 8 = 482) How many diamonds are there in a cuboctohedron? What is the total suface area of Triangles the diamonds? Height?3) What shape are the other faces (other than the (81/2)2 = (81/2/2)2 + x2 diamonds)? 8 = 2 + x2 6 = x24) What is the height of the triangle (use the x = 61/2 pythagorean theorem)? What is its area?5) What is the surface area of all the triangles? Area Of One Triangle6) What is the total surface area? 1/2 * 61/2 * 81/2 = (481/2)/2 = 4 * (481/2) Answer: 48 + 4 * (481/2) BACK
  • 436. PROBLEM • A farmer found an advertisment for a plot of land with very good soil and an asking price of $12500.00. The plot of land looked like this: • Why didnt the farmer buy the land?Hint and answer
  • 437. SOLUTIONWhat is the sum of the sides of the triangle?Does this tell you anything?Do the sum of the two sides of a triangle have to be greater or less than the length of the other?ANSWERThe sum of the two sides = 300 + 200 = 500 The sum of the two sides of a triangle has to be greater than the third side.Therefore, the piece of land was a line, not a triangle and had no area!! BACK
  • 438. PROBLEM• In a recent survey, 40% of houses contained two or more people. Of those homes containing only one person, 25% contained a male. What is the percentage of all houses which contain exactly one female and no malesHint and answer
  • 439. HINTS1) What percentage of homes contain only one person?2) 25% of the homes containing one person contain a male. Then what percent of the homes contain a female?40% contain two or more people 60% contain one person 25% of 60% contain a male 15% of total contain a male.ANSWER45% of houses contain single females. BACK
  • 440. PROBLEM• In a recent election at the Dr. John Hugh Gillis High School, Susie Cook received 542 votes, Greg MacDonald received 430 votes and Travis Austen received 130 votes. If 90% of those eligible to vote did so, what was the number of eligible votersHint and answer
  • 441. HINTS1) How many students actually voted?2) If 90% of the total number of students voted then what is the total number of students in the school?ANSWERLet x = the number of eligible voters 542 + 430 + 130 = 1102 .9 * x = 1102 x = 1224 There were 1224 eligible voters. BACK
  • 442. PROBLEM• Jill loves math but she hates this problem. Can you help her? The sum of four numbers is 64. If you add 3 to the first number, 3 is subtracted from the second number, the third is multiplied by 3 and the fourth is divided by three, then all the results will be equal. What is the difference between the largest and the smallest of the original numbers?Hint and answer
  • 443. HINTS1) Let a, b, c and d be your four different numbers.2) Then a + 3 = b - 3 = ? = ? (Fill in the question marks) Let them all equal a variable x.3) What does x equal in terms of a, b, c and d?4) a + b + c + d =64 (In terms of x what does this equation look like?5) What does x equal? What do a, b, c and d equal?6) What is the difference between a and b?ANSWERa + 3 = b - 3 = 3c = d/3 Let k equal the number all of them equal k=a+3 k=b-3 k = 3c k = d/3 a=k-3 b=k+3 c = k/3 d = 3k k - 3 + k + 3 + k/3 + 3k = 64 5k + k/3 = 64 16k/3 = 64 k = 12 a = 12 - 3 = 9 d = 3(12) = 36 36 - 9 = 27 BACK
  • 444. PROBLEM• If the five expressions 2x + 1, 2x - 3, x + 2, x + 5, and x - 3 can be arranged in a different order so that the first three have a sum 4x + 3, and the last three have a sum 4x + 4, what would the middle expression be?Hint and answer
  • 445. HINTSRearrange the expressions so that the conditions are met.ANSWER x+5 2x - 3, x + 2, x + 5, 2x + 1, x - 3 BACK
  • 446. PROBLEM • Mark has $4.50 and Jean- Martin has $3.00. Mark spends twice as much as Jean-Martin and now sees that he has half as much money left as Jean-Martin has left. How much money did Mark spend? How much money did Jean-Martin spend? How much do each of them have left?Hint and answer
  • 447. HINTS1) If Jean-Martin spends x amount of money, then how much does Mark spend?2) Two times the amount of money Mark has left, equals the amount Jean-Martin has left.3) If Jean-Martin has 3.00 - x left, how much does Mark have?4) Solve your algebraic equation for x.ANSWERMark: $4.50 J.M.: $3.00 Mark spends 2x J.M spends x 2(4.50 - 2x) = 3.00 - x 9.00 - 4x = 3.00 - x 3x = 6.00 x = 2.00 Jean-Martin spends $2.00 and has $1.00 left. Mark spends $4.00 and has $0.50 left BACK