Systems of Equations1) A vendor sells hot dogs and bags of.docxdeanmtaylor1545
Systems of Equations
1) A vendor sells hot dogs and bags of potato chips. A customer buys 4 hot
dogs and 5 bags of potato chips for $12.00. Another customer buys 3 hot
dogs and 4 bags of potato chips for $9.25. Find the cost of each item.
1)
2) University Theater sold 556 tickets for a play. Tickets cost $22 per adult
and $12 per senior citizen. If total receipts were $8492, how many senior
citizen tickets were sold?
2)
3) A tour group split into two groups when waiting in line for food at a fast
food counter. The first group bought 8 slices of pizza and 4 soft drinks
for $36.12. The second group bought 6 slices of pizza and 6 soft drinks
for $31.74. How much does one slice of pizza cost?
3)
4) Tina Thompson scored 34 points in a recent basketball game without
making any 3-point shots. She scored 23 times, making several free
throws worth 1 point each and several field goals worth two points each.
How many free throws did she make? How many 2-point field goals did
she make?
4)
5) Julio has found that his new car gets 36 miles per gallon on the highway
and 31 miles per gallon in the city. He recently drove 397 miles on 12
gallons of gasoline. How many miles did he drive on the highway? How
many miles did he drive in the city?
5)
6) A textile company has specific dyeing and drying times for its different
cloths. A roll of Cloth A requires 65 minutes of dyeing time and 50
minutes of drying time. A roll of Cloth B requires 55 minutes of dyeing
time and 30 minutes of drying time. The production division allocates
2440 minutes of dyeing time and 1680 minutes of drying time for the
week. How many rolls of each cloth can be dyed and dried?
6)
7) A bank teller has 54 $5 and $20 bills in her cash drawer. The value of the
bills is $780. How many $5 bills are there?
7)
8) Jamil always throws loose change into a pencil holder on his desk and
takes it out every two weeks. This time it is all nickels and dimes. There
are 2 times as many dimes as nickels, and the value of the dimes is $1.65
more than the value of the nickels. How many nickels and dimes does
Jamil have?
8)
9) A flat rectangular piece of aluminum has a perimeter of 60 inches. The
length is 14 inches longer than the width. Find the width.
9)
1
10) Jarod is having a problem with rabbits getting into his vegetable garden,
so he decides to fence it in. The length of the garden is 8 feet more than 3
times the width. He needs 64 feet of fencing to do the job. Find the
length and width of the garden.
10)
11) Two angles are supplementary if the sum of their measures is 180°. The
measure of the first angle is 18° less than two times the second angle.
Find the measure of each angle.
11)
12) The three angles in a triangle always add up to 180°. If one angle in a
triangle is 72° and the second is 2 times the third, what are the three
angles?
12)
13) An isosceles triangle is one in which two of the sides are congruent. The
perimeter of an isosceles triangle is 21 mm. If the.
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1. Real World
1. At a Boy Scout fund-raising dinner, Mr. Jones bought 2 adult meals and 3 child meals for $23.
Mrs. Gomez bought 4 adult meals and 2 child meals for $34. Write a system of linear equations
to represent this information and then solve the system to find the cost of one adult meal and
one child meal.
2. The costs for tickets to see a play are $15 for adults and $12 for students. A group of 11 adults
and students bought tickets for the play. If the total cost was $156, how many of each type of
tickets did they buy?
3. Ace Car Rental rents a car for $45 a day and $0.25 per mile. Star Car Rental rents a car for $35
per day and $0.30 per mile. How many miles would a driver need to drive before the cost of
renting a car at both rental agencies are the same?
2. 4. The charge for admission to the zoo is $3.25 for each adult and $1.50 for each child. On a day
when 500 people paid to visit the zoo, the receipts totaled $1275. Find the number of adult
tickets purchased that day.
5. The school that Stefan goes to is selling tickets to a choral performance. On the first day of
ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. The
school took in $52 on the second day by selling 3 senior citizen tickets and 2 child tickets. Find
the price of a senior citizen ticket and the price of a child ticket.
6. The state fair is a popular field trip destination. This year the senior class at High School A and
the senior class at High School B both planned trips there. The senior class at High School A
rented and filled 8 vans and 8 busses with 240 students. High School B rented and filled 4 vans
and 1 bus with 54 students. Every van had the same number of students as did the buses. Find
the number of students in each van and each bus.
3. Coin
7. Linda has 20 coins in her pocket. Some of them are nickels and the rest are dimes. The value of
nickels and dimes together is $1.40. How many dimes does Linda have?
8. The number of quarters that Eleanor has is 3 times the number of nickels. She has $1.60 in all.
How many of each coins of each type does she have?
9. You have a total of 21 coins, all nickels and dimes. The total value is $1.70. How many nickels
and dimes do you have?
4. 10. Greg has 20 coins in his pocket consisting of quarters and pennies. The total value of $1.88.
How many quarters and pennies do you have?
11. Frances has a total of 27 coins in her purse consisting of nickels and pennies. The coins have a
total value of $0.63. How many nickels and pennies does she have?
12. Brent is cashing in his piggy bank. It consists of a total of 81 coins that are quarters and dimes.
He receives $11.55 for the coins. How many quarters and dimes does Brent have.
5. Digit
13. The sum of two numbers is 24. One number is three times the other number. What are the two
numbers?
14. The sum of two numbers is 34. The difference of the two numbers is 14. Find each of the
numbers
15. The sum of two numbers is 45. One number is four times the other. What are the two
numbers?
6. 16. Find the value of two numbers if their sum is 12 and their difference is 4.
17. The difference of two numbers is 3. Their sum is 13. Find the numbers.
18. The sum of two numbers is 41. Their difference 11. Find the numbers.
7. Break Even
19. A local band is planning to make a compact disc. It will cost $12,000 to record and produce a
master copy, and an additional $2.50 to make each sale copy of the disc. If they plan to sell the
final product for $7.50, how many discs must they sell to break even?
20. McGuffey High School is paying $13,200 for the writing and research of their yearbook, plus a
printing fee of $25 per book. If they sell the books for $40 each, how many will they have to sell
to break even?
21. Jared has volunteered 50 hours and plans to continue volunteering 3 hours per week.
Clementine just started volunteering 5 hours per week. Find the number of weeks in which
Jared and Clementine will have both volunteered the same number of hours.
8. Wind/Current
22. Flying to Madagascar with a tailwind a plane averaged 158 km/hr. On the return trip, the plane
only averaged 112 km/hr while flying back into the same wind. Find the speed of the wind and
the speed of the plane in still air
23. Paddling in a canoe to a campsite against the current, you travel at 3.5 mph. On the return trip
(with current) you paddle at 5.7 mph. What is the speed of the canoe in still water? What is the
speed of the current?
24. Rose took a half hour to row 3 km with the current. When she returned, she took an hour and a
half. Find her rowing rate and the speed of the current.
9. 25. With a tail wind, a light plane can fly 375 km in 1 hour. Going against the wind, the plane can fly
290 km/h. What are the speeds of the wind and the plane?
26. On a canoe trip, Rita paddled upstream (against the current) at anaverage speed of 2 mi/h
relative to the riverbank. On the return tripdownstream (with the current), her average speed
was 3 mi/h. FindRita’s paddling speed in still water and the speed of the river’s current.
27. A light plane flew from its home base to an airport 255 miles away.With a head wind, the trip
took 1.7 hours.The return trip with a tailwind took 1.5 hours. Find the average airspeed of the
plane and theaverage windspeed. (HINT: rate*time = distance)