Question

The cost of constructing a wooden box with a square base varies jointly as the height of the box and the square of the width of the box. A box of height 16 inches and of width 6 inches costs $28.80. How much would a box of height 14 inches and of width 8 inches cost?

Answer 1

http://www.purplemath.com/modules/variatn.htm defines joint variation.

Hi! What you want to do is to start speaking math! Like, the cost \((C)\) varies with the product of the height \((h)\) and the width \((w)\) squared \((w^2)\) by an unknown factor of \(x\).

\(C=x\left(h\ w^2\right)\)

Then speak more math. With \(h=16\ [in]\) and \(w=6\ [in]\), \(C=$28.80\). That is
\($28.80=x\left((16)\ (6)^2\right)\)
So you can solve for your unknown factor!!

Then, just throw in the new \(h\) and \(w\). You have your \(x\) now, so you can solve for the new \(C\).