Lower Elementary:
Question: William came home at 3 PM. He spent 30 minutes playing basketball, an hour playing video games, and then he took a 90 minute nap. What time did William wake up from his nap?
Answer: 6 PM
Solution: One way to solve this problem is to calculate the total time it took for William to finish all of his activities. He spent 30 minutes playing basketball and an hour playing video games, so an hour and a half has passed. His nap was 90 minutes. There are 60 minutes in an hour, so 90 minutes is the same as an hour and a half. So, William’s nap lasted an hour and a half. Since he played for an hour and a half and slept for an hour and a half, that means that 3 hours have passed since he came home (1 ½ + 1 ½ = 3). 3 hours past 3 PM is 6 PM. So, William woke up from his nap at 6 PM.
Upper Elementary:
Question: Erin is doing random jobs to make some money. She earns $20 an hour for babysitting, $15 an hour for house cleaning, and $10 an hour watching pets. In a week, she babysat for 3 hours, she cleaned for 5 hours, and she watched pets for 2 hours. How much money did Erin make in the week?
Answer: $155
Solution: To solve this problem, first let’s find out how much Erin made with each job. She earns $20 an hour babysitting and babysat for 3 hours. 3 × 20 = 60. She earned $60 babysitting. She earns $15 an hour house cleaning and cleaned for 5 hours. 15 × 5 = 75. She earned $75 cleaning. She earns $10 an hour watching pets and watched pets for 2 hours. 10 × 2 = 20. She earned $20 watching pets. To find the total amount that Erin earned, we add the amount she made for each job together. 60 + 75 + 20 = 155. Erin earned a total of $155 doing the jobs.
Middle School:
Question: On a coordinate plane, the point (4, 5) is reflected across the y-axis, and then moved 3 units to the right and 2 units up. What are the coordinates for the position of the new point?
Answer: (–1, 7)
Solution: When a point is reflected across the y-axis, the x-coordinate changes its sign and the y-coordinate stays the same. So, after the point is reflected across the y-axis, the point is now at (–4, 5). If it moves 3 units to the right, then we add 3 to the x-coordinate. –4 + 3 = –1. After moving to the right, the point is at (–1, 5). If it moves 2 units up, then we add 2 to the y-coordinate. 5 + 2 = 7. So, after doing all of these transformations, the coordinates of the new point are (–1, 7).
Question: A number to the 12th power divided by the same number to the 9th power is 64. What is the number?
Answer: 4
Solution: Let x be the number we are trying to find. Written out, the question becomes:
x12 / x9 = 64
When dividing a number with the same base, we subtract the exponents. Since 12 – 9 = 3. So now our problem becomes:
x3 = 64
To get x by itself, we take the cubed root of both sides.
x = cubed root of 64
What number, as a factor three times, is 64? 4 × 4 = 16 and 16 × 4 = 64, so the cubed root of 64 is 4. So, x = 4.
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