Lower Elementary:
Question: Washing a load of clothes costs 5 quarters. Drying a load of clothes costs 4 quarters. How much would it cost to do 2 full loads of laundry?
Answer: 18 quarters, or $4.50
Solution: It takes 5 quarters to wash a load of clothes and 4 quarters to dry a load of clothes. So that means it takes 5 + 4 = 9 quarters to do an entire load of laundry. To find the cost of doing 2 loads of laundry, we double the cost of one load of laundry. 9 doubled is 18. It costs 18 quarters, or $4.50 to do two full loads of laundry.
Upper Elementary:
Question: Carly had $100. She spent $30 on groceries and then spent the rest on $10 gift cards. How many gift cards did Carly buy?
Answer: 7 gift cards
Solution: Carly started with $100 and then spend $30. 100 – 30 = 70. Carly had $70 to spend on gift cards. Since each gift card is $10, we divide the total by 10 to see how many gift cards she buys. 70 ÷ 10 = 7. She bought 7 gift cards.
Middle School:
Question: What is the best bargain for meat: three fourths of a pound for $2.25, one and a half pounds for $4.20, or one and three fourths of a pound for $5.04?
Answer: One and a half pounds for $4.20
Solution: One way to solve this problem is to find the unit price for each of the deals. Let’s find out how much 1 pound of meat costs in each scenario. If three fourths costs $2.25, then one fourth costs 75¢. If we multiply by 4, we see that 1 pound of meat costs $3 in the first deal. For the second deal, one and a half pounds costs $4.20. If we break $4.20 into three groups, we have that half a pound costs $1.40. By doubling this, we have that one pound costs $2.80 in the second deal. For the third deal, we have that one and three fourths pounds costs $5.04. One and three fourths is the same as seven fourths. So, if we break $5.04 into seven parts, we see that a quarter of a pound costs 72¢. If we multiply by 4, we have that one pound costs $2.88 in the third deal. So the one and a half pounds for $4.20 is the best deal
Algebra and Up:
Question: The ratio between two similar triangles is 2:3. The area of the smaller triangle is 8 square inches. What is the area of the larger triangle?
Answer: 18 square inches.
Solution: One way to solve this problem is to make a triangle that has an area of 8 square inches. The formula for the area of a triangle is 1/2 base × height. A triangle that has a base of 8 inches and a height of 2 inches will have an area of 8 square inches since (1/2) 8 × 2 = 4 × 2 = 8. Since the Ratio of the similar shapes is 2:3, that means that the similar triangle will have a height of 3 and a base of 12. Now, let’s find the area of this triangle. (1/2) 12 × 3 = 6 × 3 = 18. The area of the larger triangle is 18 square inches.
Alternatively, if the ratio of the sides of a triangle are 2:3, then that means the ratio of the areas of the triangles is the ratio squared. 2 squared is 4 and 3 squared is 9, so the ratio between the area s of the triangles is 4:9. Since the area of the smaller triangle is 8, we can set up a proportion to see than 4/9 = 8/a where a is the area of the larger triangle. Solving this proportion, we have that a = 18, so the area of the larger triangle is 18 square inches.
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