5
QuizMultiple Choice

Density and Design Problems — Quiz

Question 5 • Mathematics III

A company needs to package 2 comma 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 point 5 0 dollars , while each cylindrical container costs 0 point 7 5 dollars Which packaging should the company use to minimize cost? Explain.

Answer
A
The rectangular prism boxes should be used because they will cost the company 5 point 0 0 dollars less than using the cylindrical containers.
B
The rectangular prism boxes should be used because they will cost the company 2 point 5 0 dollars less than using the cylindrical containers.
C
The cylindrical containers should be used because they will cost the company 2 point 5 0 dollars less than using the rectangular boxes.
D
The cylindrical containers should be used because they will cost the company 5 point 0 0 dollars less than using the rectangular boxes.

Explanation

The rectangular prism boxes require 2,400 ÷ 60 = 40 boxes, costing 40 × $0.50 = $20. The cylindrical containers require 2,400 ÷ 80 = 30 containers, costing 30 × $0.75 = $22.50. The rectangular prism boxes cost $22.50 − $20 = $2.50 less, so the company should use them.

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