What is the volume of the package

Question

The sum of the length, width, and height of a rectangular package is 96 inches. If the length is 4 inches longer than five times the height and the width is 4 inches shorter than twice the height, what is the volume of the package?

Answer 1

The volume of a rectangular package V = L x H X W, where L=length, H= height and W= width.

Say the height is h inch. So the width will 2h-4 inch and length will be 5h+4 inch.

Therefore the volume is: h x (2h-4) x (5h+4)

It's given that h+2h-4+5h+4 = 96

                    Or, 8h  = 96

                          h = 96/8 = 12 inch

                          width = 2h-4 = 24-4 = 20 inch

                          length =  5h+4 = 60+4 = 64 inch

The volume is 12x20x64 = 15,360 cubic inches.

 

Answer 2

Let h be the height of the package. So then we can create two equations for length and width.

 

height= h

length= 5h + 4

width=2h - 4

 

Now we can solve for the height using the perimeter and subsequently solve for the length and width.

 

96 = h + (5h+4) + (2h-4)

96= 8h

12= h

 

length= 5(12) + 4= 64

width= 2(12)-4= 20

 

The volume of a rectangle is just multiplying the height, width, and length together.

 

V= 12*20*64= 15360 in³