College Algebra Word Problem

Question

Apiece of cardboard is 2.8 times as long as it is wide. It is to be mad into a box with an open top by cutting 2-inch squares from each corner and folding up the sides. Let X represent the width(in inches) of the original piece of cardboard.

(a). What is the length and width when volume is 320?

(b). what is the length and width when volume is between 400 and 500?

Answer 1

L=2.8X

2(L-4)(X-4) = volume

= 2(2.8X-4)(X) = 320

2(2.8z^2 -4X) = 320

5.6X^2 -8X = 320

5.6X^2 -8X -288=0

X = 8/11.2 + or - (1/11.2)sqr(8^2 + 4(5.6)(288))

L= 2.8X