Story problem in algebra

Question

A box’s volume is equal to 600 cubic inches. If the width of the box is 7 inches less than the length, and the height is 10 inches less than the length, find the dimensions of the box.

Answer 1

Volume = Lwh = 600 in³

w = L-7

h = L-10

 

L(L-7)(L-10) = 600

L³ - 17L² + 70L = 600

Note:  L must be more than 10 inches or the volume will be negative.

Let's try L = 15:  15(15-7)(15-10) = 600

                         15(8)(5) = 600

                         600 = 600

L = 15 inches

w = L-7 = 8 inches

h = L-10 = 5 inches