please help find volume of brick. details below

Question

the width of a brick is half the length, which is 2 inches less than four times the height. if the sum of the three dimensions is 14.5 in find the volume of the brick

Answer 1

Let w = the width, let L = the length, and let h = the height

 

w = 1 L         L = 4h-2         L+w+h=14.5 (equation #3)

       2

 

In equation #3, replace "L"  with 4h-2, replace "w" with 1/2 L, then replace "L"

with 4h-2.

 

4h - 2 + 1/2(4h-2) + h = 14.5

4h - 2 + 2h - 1 + h = 14.5

                          7h = 17.5

                           h = 2.5       L = 4h-2 =4(2.5)-2 = 8     w = 1/2 (8) = 4

 

V = lwh

V = 8(4)(2.5)

V = 80 cubic inches