Question

A company is designing a box for dry pasta in the shape of a rectangular prism. The length is 2 inches more than twice the width, and the height is 3 inches more than the length. Write an expression in terms of the width, for the volume for the box.

Answer 1

(2W + 2)(2W + 5)W = 4W³ + 14W² +10W (that first exponent is a 3, doesn't look very clear on my screen)

Explanation:

Let W be width, L be length, and H be height.

L = 2W + 2

H = L + 3 but L = 2W +2, so substitute.

H = (2W +2) + 3

H = 2W + 5

and of course W = W

The volume is L x H x W = (2W + 2)(2W + 5)W

= (4W² + 14W +10)W

= 4W³ + 14W² +10W (that first exponent is a 3, doesn't look very clear on my screen)