Lower Elementary:
Question: A 12-inch piece of string is cut into 3 pieces. One piece is 2 inches and another piece is 7 inches. How long is the third piece?
Answer: 3 inches
Solution: We have the whole, 12 inches, and we have two of the three parts, 2 inches and 7 inches. To find the third part, subtract the other parts from the whole. 12 inches – 2 inches = 10 inches. 10 inches – 7 inches = 3 inches. The third piece is 3 inches long.
Upper Elementary:
Question: There are 120 apple trees in a field. 10 apples are picked from each tree and the sold at a local market for $2 an apple. How much money is made from selling all of the apples?
Answer: $2,400
Solution: First we need to calculate the number of apples picked from the trees. There were a total of 120 trees and 10 apples were picked from each tree. That means a total of 1,200 apples were plucked (120 × 10 = 1,200). Each apple was sold for $2. To find the money made from selling the apples, multiply the price of each apple by the total number of apples. 1,200 × 2 = 2,400. $2,400 is made from selling the apples.
Middle School:
Question: A trumpet is on sale for 15% off the original price. If the original price is $400, what is the discounted price of the trumpet?
Answer: $340
Solution: First, we have to calculate the discount amount. To find the discount amount, multiply the discount percent and the original price. 400 × 0.15 = 60. The discount amount is $60. To find the discounted price of the trumpet, subtract the discount amount from the total. 400 – 60 = 340. The trumpet costs $340.
Algebra and Up:
Question: Two shirts and one jacket cost $52. Three shirts and two jackets cost $89. How much would one shirt and one jacket cost separately?
Answer: One shirt is $15 and one jacket is $22
Solution: Let s be the cost of a shirt and let j be the cost of a jacket. Writing the question as a system of equations, we have:
2s + j = 52
3s + 2j = 89
One way to solve this problem is to use elimination. Start by multiplying the top row by –2
–4s – 2j = –104
3s + 2j = 89
Add the equations together.
–s = –15
Multiply both sides by –1.
s = 15
One shirt costs $15. Substitute in this value into one of the original equations to find the cost of a jacket.
2(15) + j = 52
30 + j = 52
j = 22
One jacket costs $22.
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