Lower Elementary:
Question: Becky bought 24 eggs. She used half of the eggs on Saturday and then used half of what was remaining on Sunday. How many eggs does she have left?
Answer: 6 eggs
Solution: Becky started with 24 eggs. She used half of them on Saturday. Half of 24 = half of 20 + half of 4 = 10 + 2 = 12. Becky had 12 eggs. She then used half of those remaining eggs on Sunday. Half of 12 = half of 10 + half of 2 = 5 + 1 = 6. Becky has 6 eggs left.
Upper Elementary:
Question: Jeremy bought 2 pieces of candy for 75¢ each and 3 bags of chips for $1.25 each. If he paid $10, how much change will Jeremy get back?
Answer: $4.75
Solution: First, we need to find how much money the candy and chips cost altogether. He bought 2 pieces of candy for 75¢. 75 doubled is 150, so Jeremy spent $1.50 on candy. He also bought 3 bags of chips for $1.25 each. Counting by 125, three times, we have 125, 250, 375. So, the chips cost a total of $3.75. In total, Jeremy spent $1.50 + $3.75 = $5.25 on candy and chips. If he paid $10, then he would get $4.75 back in change.
Middle School:
Question: Dillan is trying to find shade. He sees a 24-foot tree and sees that it casts a 10-foot shadow. When Dillan sits down, he is 3 feet tall. What is the farthest distance away from the base of the tree that Dillan can sit and still be in the shade?
Answer: 8.75 feet
Solution: One way to solve this problem is to see how long a shadow Dillan will cast when he sits down and then subtract that from the length of the shadow that the tree casts. We can use ratios to compare the height to the length of the shadow. For the tree, the ratio is 24/10 = 12/5. Let x be the length of Dillan’s shadow. The ratio for Dillan is 3/x. Let’s compare the ratios to solve for x.
12/5 = 3/x
To go from 12 to 3, we divide by 4. So, to get from 5 to x, we divide by 4. 5 ÷ 4 = 1.25. Dillan casts a 1.25-foot shadow when sitting. If the tree casts a 10-foot shadow and Dillan casts a 1.25-foot shadow when sitting, then Dillan can sit 10 – 1.25 = 8.75 feet away from the base of the tree and still sit in shade.
Algebra and Up:
Question: The quantity of five times a number plus seven cubed is seven hundred twenty-nine. What is the number?
Answer: 2/5
Solution: Let x represent the number we are trying to find. If we write out the question above, we have:
(5x + 7)3 = 729
Let’s take the cube root of both sides.
5x + 7 = 9
Subtract 7 from both sides.
5x = 2
Divide by 5
x = 2/5
The mystery number is 2/5.
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