Lower Elementary:
Question: Bobby ate twice as many crackers as Tina. Tina ate twice as many crackers as Sam. If Sam ate 4 crackers, how many crackers did Bobby eat?
Answer: 16 crackers
Solution: Tina ate twice as many crackers as Sam. 4 doubled = 8. Tina ate 8 crackers. Bobby ate twice as many crackers as Tina. 8 doubled = 5 doubled + 3 doubled = 10 + 6 = 16. Bobby ate 16 crackers.
Upper Elementary:
Question: Reid slept for 10 hours. He slept from 10:49 PM to 6:04 AM and then took a nap later in the day. If he woke up from his nap at 2:00PM, what time did he start taking his nap?
Answer: 11:15AM
Solution: First, let’s find out how long Reid slept during the night. If we count by an hour starting at 10:49, we have 10:49, 11:49, 12:49, 1:49, 2:49, 3:49, 4:49, 5:49. This is 7 hours. From 5:49 to 6:00 is 11 minutes and from 6:00 to 6:04 is 4 minutes. This means that Reid slept for 7 hours and 15 minutes during the night. If he slept for 10 hours, that means his nap lasted for 2 hours and 45 minutes. If Reid woke up at 2:00PM, then we count backwards to see what time Reid fell asleep. Counting backwards by 2 hours from 2:00PM is 12:00PM and then 45 minutes before that is 11:15AM. This means Reid started his nap at 11:15AM.
Middle School:
Question: Megan will use 40% of the money in her bank account to pay her portion of the rent. She will use one fourth of the money in her bank account to pay for groceries and gas. She is saving the remaining $385 in case of an emergency. How much total money does Megan have in her bank account?
Answer: $1,100
Solution: One way to solve this problem is to find the portion of her bank account that Megan is planning on saving. One fourth can be written as 25%. Her rent and groceries and gas make up 40% + 25% = 65% of the money in her bank account. This means that 100% – 65% = 35% of the money in Megan’s bank account she is planning on saving. She is planning on saving $385. 35% of what number is 385? Percent means for each hundred. 35% of 100 is 35, so 35% of 1,000 is 350. Since 350 + 35 = 385, this means that 35% of 1,100 is 385. This means that Megan has $1,100 in her bank account.
Algebra and Up:
Question: X is inversely proportional to the square of Y. If X = 0.75 when Y = 2, what is Y when X = 0.12?
Answer: Y = 5
Solution: X is inversely proportional to the square of Y. This means that X = k/Y2 where k is a constant. To find k, we need to use the fact that X = 0.75 when Y = 2.
X = k/Y2
Substitute the values.
0.75 = k/22
Simplify.
0.75 = k/4
If we rewrite 0.75 as a fraction, we have
3/4 = k/4
So k = 3. Now that we have k, we have that the relationship between X and Y is X = 3/Y2. When X = 0.12 = 3/25, this becomes
3/25 = 3/Y2
Since the numerators are the same, the denominators must also be the same. So,
25 = Y2
Take the square root.
5 = Y
(925) 292-8854
