Lower Elementary:
Question: Christian has twice as much money as his sister. He spends $3 to buy some snacks. If his sister has $16, how much money does Christian have after buying the snacks?
Answer: $29
Solution: Christian has twice as much money as his sister. 16 doubled = 10 doubled + 6 doubled = 20 + 12 = 32. So Christian has $32. He spends $3 buying snacks, so Christian now has 32 – 3 = $29.
Upper Elementary:
Question: Aaron ate 4/5 of a pie. Brittney ate 8/9 of a pie. Carlos ate 9/10 of a pie. Who has the most pie left over?
Answer: Aaron
Solution: To find how much pie is left over from each person, subtract the part that they ate from 1, or a whole. Aaron: 1 – 4/5 = 1/5. Brittney: 1 – 8/9 = 1/9. Carlos: 1 – 9/10 = 1/10. We want to find the largest fraction because that will be the pie that has the most left over. The denomination that has the biggest piece is 1/5, so Aaron has the most pie left over.
Middle School:
Question: For the first six days of the week, Jenna posted 3 photos a day on social media. How many does she need to post on the seventh day to have an average of 4 photos posted a day for the week?
Answer: 10 photos
Solution: To have an average of 4 photos a day for the week, Jenna would have to take a total of 28 photos (7 days, 4 photos a day, 7 × 4 = 28). Since she took 3 photos a day for the first 6 days, she took 18 photos in the first 6 days. So to have an average of 4 photos a day, she needs to take 10 photos on the seventh day (28 – 18 = 10).
Algebra and Up:
Question: Two beach balls are similar. The larger one has a volume of 972π cubic inches. If the ratio between them is 3:2, what is the radius of the smaller beach ball?
Answer: 6 inches
Solution: One way to solve this problem is to find the radius of the larger beach ball and then use the ratio between the beach balls to find the radius of the smaller beach ball. The volume of a sphere is V = 4/3πr3.
972π = 4/3πr3
Divide both sides by π.
972 = 4/3r3
Multiply both sides by 3/4.
729 = r3
Take the cubed root of both sides.
9 = r.
The radius of the larger sphere is 9 inches. The ratio between the two beach balls is 3:2. So the radius of the smaller beach ball is 6 inches, since 9:6 = 3:2.
