Answers to Problems of the Week - December 13 to December 19

Rewards for Problems of the week:

5 stars for the correct answer at your level; 10 stars for the next level; 20 stars for 2+ levels up.

Lower Elementary:

Question: There are 51 kittens in a shelter. Seventeen of the kittens have black fur, 14 of the kittens have orange fur, and the rest of the kittens have white fur. How many kittens in the shelter have white fur?

Answer:  20 white kittens                             

Solution:  To find the number of kittens with white fur, we take the total number of kittens and subtract the number of each other color: 51 kittens – 17 black kittens = 34 kittens, and 34 kittens – 14 orange kittens = 20 white kittens.

Upper Elementary:

Question: It takes Andrew 25 minutes to build one bird feeder. If he needs to build seven bird feeders and has already finished three, how much longer will it take Andrew to finish the bird feeders?

Answer:  1 hour and 40 minutes

Solution:  Andrew needs to build 7 bird feeders in total and has already made 3 of them. That means he has 7 – 3 = 4 left to build. Each bird feeder takes 25 minutes, so the remaining bird feeders will take Andrew 25 minutes × 4 = 100 minutes (or 1 hour and 40 minutes) to finish.             

Middle School:

Question: After using her phone for 36 minutes, Scarlett notices that her battery indicator says that it is five-eighths full. If the battery was fully charged when Scarlett started using it, then how many minutes will the battery last on a full charge in total?

Answer:  96 minutes, or 1 hour and 36 minutes

Solution:  Since the battery went from full to five-eighths full in 36 minutes, that means that Scarlett used three-eighths of the battery. If 36 minutes is three-eighths of the battery, then 36 ÷ 3 = 12 minutes is one-eighth of the battery. That means that a full charge will last 12 × 8 = 96 minutes, or 1 hour and 36 minutes in total.

Algebra and Up:

Question: Mason and Natalie are painting fences. Mason can paint a fence in an hour. If Mason and Natalie work together, they can paint two fences in 1 hour and 12 minutes. How long will it take for Natalie to paint one fence by herself.

Answer:  90 minutes

Solution:  The sum of Mason’s and Natalie’s fence-painting rates is 2 fences/72 minutes , or 1 fence/36 minutes. Mason can paint a fence in an hour, so if we subtract his rate from the combined rate, we’ll find the rate at which Natalie can paint a fence by herself.

1 fence/36 minutes  – 1 fence/60 minutes =

5 fences/180 minutes – 3 fences/180 minutes = 2 fences/180 minutes

So, Natalie can build 2 fences in 180 minutes, or 1 fence every 90 minutes.

Challenge problem to take home. 5 stars for the correct answer. 

What is the minimum number of matchsticks that must be removed from this arrangement to leave exactly two squares?

Answer: 2 matchsticks