PLEASE HELP! A piece of cardboard is three times as long as it is wide. It is made into a box with an open top...

Question

>How do I set this problem up and solve it?

FULL QUESTION:

A piece of cardboard is three times as long as it is wide. It is made into a box with an open top by cutting 4-inch squares from each corner and folding up the sides. Let x represent the width of the original piece of cardboard.

1) Represent the volume of the open top box as a function of x.

2) For what dimensions of the original piece of cardboard will this box have a volume of 112 square inches? Find your answer using algebra.

Answer 1

(1)

The width is x...

the length is 3x....

Cutting....

The width becomes (x-8)

the length becomes (3x-8)

the volume of the box is 4(x-8)(3x-8)

(2)

112 = 4(x-8)(3x-8)

28 = (x-8)(3x-8)

28 = 3x^2 - 32x + 64

0 = 3x^2 - 32x + 36

quadratic formula says

[32 +or- sqrt ( 32^2 - 4(3)(36))] / 6 =

[ 32 +or- sqrt( 1024 - 432)]/6 =

[ 32 +or- sqrt( 592) ]/ 6 =

[ 32 +or- 4 sqrt(37) ] / 6 =

16 +or- 2 sqrt(37) / 3