Lower Elementary:
Question: How many total shoes would a family of 6 have if every family member has 2 different pairs of shoes each?
Answer: 24 shoes
Solution: All 6 members have 2 different pairs of shoes. 6 doubled is 12. There are 2 shoes in a pair. 12 doubled is 24 shoes.
Upper Elementary:
Question: Max ordered 3 sundaes for $5.75 each. How much change would he get if he pays $20?
Answer: $2.75
Solution: First find the total amount of money Max spent. $5.75 × 3 = $17.25. Then to find the change subtract the total from $20. $20 – $17.25 = $2.75
Middle School:
Question: A group of 20 friends go out to dinner. They all agree to leave a 20% tip. If their bill comes to $175, how much would each person pay for tip?
Answer: $1.75
Solution: First find how much of a total tip the group should leave. Percent means for each hundred, so 20% is 20 for each hundred. 75 is 3/4 of a hundred, and 3/4 of 20 is 15. By breaking 175 into 100 + 75, we see that 20% of 175 is 20 + 15 = 35. We can also calculate it by multiplying the tip percent to the bill. $175 × 20% = $175 × 0.2 = $35. So they will leave a $35 tip. Divide that by the number of people to see how much each person pays. $35 ÷ 20 = $1.75. So each person pays $1.75. Alternatively, since they agree to pay a 20% tip and there are 20 people, that means each person is responsible for 1% of the total bill. 1% of $175 is $1.75.
Algebra and Up:
Question: Nora needs to make a triangle out of 3 different pieces of string. The first piece is 4 inches long and the second piece is 9 inches long. What is the range of lengths the 3rd piece of string can be?
Answer: Greater than 5 inches and less than 13 inches.
Solution: One property of triangles is that the sum of 2 sides must be larger than the 3rd side. Thus we have 2 possibilities:
1) The 9 inch long side is the longest side. That means that 4 plus the length of the 3rd side must be more than 9. As an inequality, that is 4 + L > 9, where L is the length of the 3rd side. Solving for L, we get that L > 5, so the 3rd side must be greater than 5.
2) The 3rd side is the longest side. That means than 4 + 9 must be greater than the 3rd side. As an inequality, 4 + 9 > L, where L is the length of the 3rd side. So 13 > L, which means the 3rd side must be smaller than 13.
Combining both of these results, we have that 5 < L < 13, or that the length of the 3rd side must be greater than 5 inches but less than 13 inches.
