Lower Elementary:
Question: Fred took the train and the bus to get home. The train left at 2:15 PM. He rode the train for 35 minutes. He then walked 5 minutes to the bus stop, where he immediately boarded the bus. He rode the bus for 25 minutes. After he got off the bus, he walked 10 minutes to his home. What time did Fred arrive home?
Answer: 3:30 PM
Solution: Start at 2:15 PM. The train ride was 35 minutes, which means Fred got off the train at 2:50 PM. He walked 5 minutes to the bus stop, so Fred got to the bus stop at 2:55 PM. The bus ride was 25 minutes, so Fred got off the bus at 3:20 PM. After walking the rest of the way home, Fred got home at 3:30 PM.
Upper Elementary:
Question: Brenda is selling apples. She started with 200 apples at the beginning of the day. She sold 1/5 of her apples to her first customer. Her second customer bought 2 dozen. How many apples does Brenda have after selling to the second customer?
Answer: 136 apples
Solution: 1/5 of 200 is 40. Brenda sold 40 apples to her first customer. One dozen is 12, so 2 dozen is 24. She sold 24 apples to the second customer. This means that she sold a total of 64 apples to her first two customers. 200 – 64 = 136. Brenda has 136 apples left.
Middle School:
Question: Mr. Norman gave a math test that had 20 questions. He also made a deal with his students: if they turned in all of their homework for the month, then he would add 5% to their exam score. For example, if a student received a 70% on the exam and turned in all of their homework, they would receive a 75% for their final score. Zack turned in all of his homework for the month, so he ended up with a final score of 85% on the math test. How many problems did Zack get correct on the math test?
Answer: 16 problems
Solution: Because Zack turned in all of his homework for the month, he received an extra 5% on his final score. This means that Zack got 80% on the exam before the extra 5% was added. To find out how many questions Zack got correct, we have to find 80% (or 4/5) of 20. One way to do this is to break 20 into 5 equal groups, and find out how many are in 4 of them. If we break 20 into 5 equal groups, then each group will have 4 in them. In four groups, there would be 16 (4 × 4). Zack got 16 problems correct on his exam.
Algebra and Up:
Question: The average of 20 numbers is 40.5. When the smallest number is removed, the average of the remaining numbers is 42. What was the value of the number that was removed?
Answer: 12
Solution: First, we need to find what the sum of the 20 numbers was. To do that, take the average and multiply it by the total number of numbers. The sum of the 20 numbers is 810 (20 × 40.5). When we remove the smallest number, we have 19 numbers left. The sum of the remaining numbers after the smallest number was removed is 798. (19 × 42). If we subtract the sums, we will find the value of the number that was removed. 810 – 798 = 12. The number that was removed was 12.
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