# Write an equation that gives Cost of box with given volume

#### Bobbie

My problem is: A closed box with a square base is to have a volume of 24 cubic feet. The material for the sides, top, and base costs $0.25,$0.50, and $1.00 per square foot, respectively. Write an equation that gives the cost, C, of the box if the length of one side of the base of the box is x feet I have C = x(24 - 3x)^3, I dont think I understand the question very well. #### stapel ##### Super Moderator Staff member Re: Write an equation that gives Cost of box with given volu Bobbie said: I have C = x(24 - 3x)^3, I dont think I understand the question very well. How did you arrive at this equation? What was your logic? How are the prices included? How does this relate to the surface areas (and costs) of each side? Thank you. Eliz. #### TchrWill ##### Full Member Re: Write an equation that gives Cost of box with given volu Bobbie said: My problem is: A closed box with a square base is to have a volume of 24 cubic feet. The material for the sides, top, and base costs$0.25, $0.50, and$1.00 per square foot, respectively.

Write an equation that gives the cost, C, of the box if the length of one side of the base of the box is x feet

I have C = x(24 - 3x)^3, I dont think I understand the question very well.
x = the length and width of the box as it was specified to be a square base.
y = the depth of the box = 24/x^2
Assuming the box is a typical box with 4 flaps forming both the bottom and top of the box, meaning that both the bottom and top have 4 flaps measuring x by x/2.
Therefore, the total cost of the box is C = [.25(4x(24/x^2)] + .50(2x^2) + 1(2x^2).

I'll let you expand and simplify the end result.