Answers to Problems of the Week - April 25 to May 1

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.

Middle School:

Question: John is growing broccoli in his garden. He plants the broccoli in the morning on April 1. 96,480 minutes later, he harvests the broccoli. On what date does John harvest the broccoli?

(You may look up how many days are in each month.)

Answer:   June 7

Solution:  If we divide 96,480 minutes by 60 minutes, we find that John harvested the broccoli 1,608 hours after he planted it. 1,608 hours ÷ 24 hours = 67 days. So, John harvested the broccoli on June 7, 67 days after April 1.

Algebra and Up:

Question: A strawberry has 1 seed per 5 square millimeters on its surface. Use the formula for the surface area of a cone—surface area = πr(r+sqrt[h² + r²])—to approximate the number of seeds on an almost-cone-shaped strawberry whose height is 36 mm and whose diameter at its widest is 54 mm. Round your answer to the nearest whole number.

Answer:  1,221 seeds

Solution: 

Answers may vary, depending on where in the process you round. Since the diameter of the strawberry is 54 mm, its radius is 27 mm. When we substitute those values into the equation, we find that the surface area of a cone with the same dimensions is 1,944π square millimeters. If we divide that by 5, we get 388.8π, or about 1,221. So, we can approximate that the strawberry has 1,221 seeds.

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

The following puzzle contains nine spaces, which you need to fill with the digits 1 to 9. You have to use each number and you can only use each number one time! Can you fill the spaces with the digits 1 to 9 so that the number sentences are all true?

Answer: