How do I solve this problem?

Question

im having trouble on my Precalc homework. This is the problem: “a box is formed by removing squares of side length x inches from each corner of a rectangular piece of cardboard 10 inches wide by 16 inches long. Determine x so that the volume of the resulting box is 137.5 in³

 

im so confused

Answer 1

The formula for volume, V, is   depth x width x length.

 

The depth is x.  With the squares cut out, the width is reduced to 10 - 2x  and the length is reduced to 16- 2x.

 

The working equation is then  137.5 = x (10- 2x) (16 - 2x)

 

This is a general cubic so it must be solved using a graphing calculator.  There are actually two values of x which solve this equation.  There are x = 1,53 and x = 2.5  The latter is exact.