Lower Elementary:
Question: Quinten sold 50 cups of lemonade for $2 a cup. He spent $35 of what he earned from selling the lemonade on a pair of pants. How much money does Quinten have left?
Answer: $65
Solution: First we need to find out the amount of money Quinten earned from selling lemonade. Since he sold lemonade for $2 a cup, to find out how much he earned, we can double the amount of glasses he sold. 50 doubled is 100. He earned $100 selling lemonade. Since he spent $35, subtract 35 from 100 to see how much money Quinten has left. 100 – 35 = 65. Quinten will have $65 left.
Upper Elementary:
Question: Valery is making bags of seeds so that she has meals ready for each of her birds. She has to put 454 seeds into bags. She accidentally drops 6 of the seeds and so she doesn’t use them. If she makes 7 bags, how many seeds are there in each bag?
Answer: 64 seeds
Solution: After dropping 6 seeds, Valery has a total of 448 seeds to put into bags(454 – 6).To see how many seeds are in each bag, divide by the number of bags. 448 ÷ 7 = 64. There are 64 seeds in each bag.
Middle School:
Question: In a 36 ounce slushy, Jake decides to mix flavors. He puts in a third cherry, a forth blueberry, and the rest he filled with strawberry flavor. How many ounces of the slushy is strawberry flavored.
Answer: 15 ounces
Solution: First, we need to find the fractional part of the slushy that is strawberry flavored. To find the fractional part, take the whole and subtract the sum of the other parts. 1 – 1/3 – 1/4. In order to subtract the fractions, all need to have the same denominator, or the same name.
1 – 1/3 – 1/4 = 12/12 – 4/12 – 3/12 = 12/12 – 7/12 = 5/12.
5/12 of the slushy is strawberry flavor. To find how many ounces of slushy that is, multiply the total ounces by the fractional part. 36 × 5/12 = 15. Jake’s slushy contains 15 ounces of strawberry flavor.
Algebra and Up:
Question: Find the number(s) that will satisfy the following condition.
Half of a number times the quantity of the same number minus seven is the same number plus eighteen.
Answer: –3, 12
Solution: Let x represent the number. The problem becomes
(1/2)x(x – 7) = x + 18
One way to solve this problem is to multiply both sides by 2 so the fraction cancels out.
x(x – 7) = 2x + 36
Distribute the x.
x2 – 7x = 2x + 36
Subtract 2x and subtract 36 from both sides.
x2 – 9x – 36 = 0
Factor the quadratic.
(x – 12)(x + 3) = 0
x = –3, 12
The solutions are –3 and 12.
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