October ProblemsMP2 Reason abstractly and quantitatively
Mrs. Hernandez’ Change10/1Mrs. Hernandez bought several items, all the sameprice. The number of items was equal to the cost ofeach item in cents. The change that Mrs. Hernandezreceived from $10 was $1 and 7 coins totaling less than$1. How much did each item cost?
Watching Water Evaporate10/2 Alice has just finished washing clothes in a 20-gallon tub and must now throw out the wash water. She pours half the water on the ground to evaporate. After it evaporates, she will again pour out half the water that is left in the tub. How many times will she pour out the water before the tub is empty?
Raise-Cut ~ or ~ Cut-Raise?10/3Suppose your salary could be raised 10% and then amonth later reduced by 10%. Or suppose that you maychoose to have the cut first, followed by the raise onemonth later. Which option is better? Why?
Will Wants His Watch Back10/4 Two boys are discussing money. Will:“How about lending me $10?” Tyler: “I can’t; I spent some of it.” Will:“How much did you spend?” Tyler:“Exactly 1/4 of what I have left.” Will: “Good. That leaves you with just what I need to get my watch back from the watchmaker.” How much money did Tyler have left?
Reel It In!10/9Jake caught a fish. To win a contest, his fish had toweigh more than the biggest one, which weighed 4pounds. Jake’s fish was hard to weigh. See if you canfigure out its total weight. The tail weighed 9 ounces,the head weighed as much as the tail and half thebody, and the body weighed as much as the head andtail together. What was the weight of the fish?
2 Keepn It Real! + 4 5 -10/10 3 Using only the digits 2, 3, 4, and 5 and the two mathematical symbols “+” and “–” each once and only once, create a true mathematical sentence. For example, 2 + 3 = 45 uses all the digits and symbols once and only once, but it is not a true mathematical sentence. You may not use any other mathematical symbols or digits.
Minimize it! 10/11Let A, B, and C represent different digits greater than 0.Determine the minimum value of the expression below.(Note: for ABC, A simply signifies a number that is the hundreds digit,B is the tens digit, and C is the ones digit—they are not multiplied.)
Pocket Change10/12I have 6 coins in my pockettotaling $1.15, but I cannot makechange for a dollar, half dollar,quarter, dime, or nickel. Whatcoins do I have in my pocket?
Counting Rectangles10/15The figure below is composed of congruent squares.How many rectangles are in the figure?
Circumference River and 10/16 Square Root BridgeThe width of the Circumference River is 3100 meters.The Square Root Bridge spans the CircumferenceRiver. If 1/8 of the bridge stands on land on one side ofthe river, and 1/10 of the bridge stands on land on theother side, how long is the Square Root Bridge?
A Paint Predicament 10/17A box (shown here as a rectangularprism) is 3 units by 4 units by 5 units.If the box is composed of unit cubesand completely dipped in paint, howmany unit cubes will have no paint onany of their faces?
What’s the Relation? 10/18If the radius of a circle isdoubled, what happens tothe area? What happensto its circumference?
Sports Confusion10/19There are 40 kids in gym.• 10 play football, soccer and basketball• 15 play football and soccer• 24 play football only• 22 play soccer only• 14 play football and basketballHow many kids are only on the basketball team?
The Prime Difference10/22Which of the following numbers:1, 2, 7, 8, or 10 cannot be thedifference of two prime numbers?Explain your reasoning, andprovide a counterexample foreach number that can be thedifference between two primes.
Tennis, Anyone?10/23 Think about a typical can containing three tennis balls. Which is greater, the height of the can or the circumference of the base of the can? (Ignore the thickness of the plastic.) Make an estimated guess first. Then use mathematics formulas and/or actual measurement to verify your guess.
Prime Number Constraints 10/24Find the sum of the least andgreatest two-digit prime numberswhose digits are also prime.Hint: 0 and 1 are not prime numbers.
Extend the Sequence10/25Find the next three numbers in the specialsequence of numbers.3, 1, 4, 1, 5, 9, 2, 6, 5, ___, ___, ___
Decoding the Riddle 10/26 Remove “twelve letters” to reveal two hidden numbers. What are the two hidden numbers? You may have to reorder the letters.(Hint: In this puzzle, “twelve letters” ≠ 12)
These Shoes Were Made for Walking10/29 You begin walking on a road. You travel 78 feet during the first minute, 85 feet the second minute, 92 feet the third minute, increasing by 7 feet each minute. If the total time you traveled is 8 minutes, how far did you walk?
Find the Missing Number10/30Based on the numbers in the first three 2 ×2 grids,determine the missing number in the fourth number grid.
Fraction Frustration10/31Find the value of the expressionabove. Your answer must be insimplified fractional form.