I need help and better understanding of this math problem.

Question

The width of a brick is half the length, and the length is 2 inches less than four times the height. If the sum of the three dimensions is 21.5 inches, find the volume of the brick. Simplify your answer

Answer 1

Hi Idalis,

 

The width is described in terms of length.

The length is described in terms of height.

 

So, let the height be h.

 

The length is 2 inches less than four times the height, or 4h-2.

 

The width is 1/2 the length, or (1/2)(4h-2) or 2h-1.

 

The sum of the dimensions is 21.5

 

So h + 4h - 2 + 2h - 1 = 21.5

 

7h - 3 = 21.5

 

7h = 24.5

 

h = 3.5

 

So length is 4(3.5) - 2 = 14 - 2 = 12

 

The width is half of 12 = 6

 

The volume is then lwh = 12(6)(3.5) = 252 cubic inches

 

Hope this helps.  :)