You are building a rectangular sandbox for a children's playground. The width of the sandbox is 4 times its height. The length of the sandbox is 8 ft more than 2 times its height. You have 40 ft3 of sand available to fill this sandbox. What are the dimensions of the sandbox?

In order to solve for the volume, we have to form a couple equations from the given:

w = 4h - "The width of the sandbox is 4 times its height."

l = 2h + 8 - "The length of the sandbox os 8 ft more than 2 times its height."

w * l * h = 40 - "You have ft^3 of sand available to fill this sandbox"

Alter the values of 'w' and 'l' in 'w * l * h = 40':

(4h) * (2h + 8) * h = 40

Multiply:

(8h^2 + 32h) * h = 40

8h^3 + 32h^2 = 40

Divide all the numbers by eight:

h^3 + 4h^2 = 5

Factor the h^2 out:

h^2 (h + 4) = 5

h = 1 (This looks like the only possible number)

We now know that h = 1.

Recall the equations we formed at the start.

w = 4 (1) = 4

l = 2 (1) + 8 = 10

The height is 1 foot, the width is 4 feet, and the length is 10 feet.