# Solutions

Excellent! Are you ready to check your child’s answer? Look below to see if their solution matches ours.

**Lower Elementary:***Answer:* 2-cup molds*Solution:* We can count to 14 by 2s (2, 4, 6, 8, 10, 12, 14), but we can’t count to 14 by 3s (3, 6, 9, 12, 15). So, if Lily wants to use all 14 cups of jello, she’ll need to use the 2-cup molds.

**Upper Elementary:**

*Answer:*

^{1}/

_{3}of the flies

*Solution:*After the frog eats half of the flies, the other half of the flies are left. The toad therefore eats a third of a half of the flies, and a third of a half is a sixth. Since

^{1}/

_{2}+

^{1}/

_{6}=

^{2}/

_{3}, that means

^{1}/

_{3}of the flies are left at the pond.

**Middle School:**

*Answer*

*:*3 minutes and 20 seconds

*Solution:*The tub fills at a rate of 24 – 6 = 18 gallons per minute. Since the tub holds 60 gallons in total, it’ll take 60 ÷ 18 = 3

^{1}/

_{3}minutes—or 3 minutes and 20 seconds—to overflow.

**Algebra and Up:**

*Answer:*3 apples

*Solution:*This is a Caeser cipher—each letter has been shifted the same number of positions. One way to solve it is to look at the first word in the last sentence, which is a question. We can reason that KRZ must be “who,” “why,” or “how” because those are the three-letter words that begin questions. If we test those words by shifting the letters, we find that the word is “how” and that shifting each letter 3 positions backward decodes the cipher. The problem decodes to “Sally has 2 apples. Timmy has 5 apples. How many more apples than Sally does Timmy have?” The answer is 3 apples.