Question

A company needs to package 2,400 pencils. A box in the shape of a rectangular prism can hold 60 pencils. A cylindrical container can hold 80 pencils. Each box costs the company $0.50, while each cylindrical container costs $0.75.
Which packaging should the company use to minimize cost? Explain.

A. The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.

B. The cylindrical containers should be used because they will cost the company $2.50 less than using the rectangular boxes.

C.The rectangular prism boxes should be used because they will cost the company $5.00 less than using the cylindrical containers.

D. The cylindrical containers should be used because they will cost the company $5.00 less than using the rectangular boxes.

Answer 1

It is A. Just took the test.

Answer 2

Each rectangular prism box costs the company $0.50, while each cylindrical container costs $0.75. You have to count how many boxes or cylindrical containers the company should buy and what is the total cost in each case.

1. 2,400 : 60 = 40 - the amount of rectangular prism boxes that can contain 2,400 pencils.

$0.50 · 40 = $20 - the total cost if packing in boxes.

2. 2,400 : 80 = 30 - the number of cylindrical containers that can contain 2,400 pencils.

$0.75 · 30 = $22.50 -  the total cost if packing in containers.

Therefore, $20 < $22.50 and the difference is $2.50.

Answer: choice A - The rectangular prism boxes should be used because they will cost the company $2.50 less than using the cylindrical containers.