Question

The height of a box that carol is wrapping is 7 inches more than the width of the box. the length is 2 inches less than twice the width. the volume of the box is 1,680 cubic inches. what are the dimensions of the box

Answer 1

The volume of the box is L * W * H = 1680
Let the width be W. But Height, H, = W + 7 and Length, L, = 2W - 2
So we have (2W - 2) * W * (W + 7) = 1680
So we have (2W^2 - 2W)(W + 7) = 1680
2W^3 - 2W^2 + 14W^2 - 14W = 1680
2W^3 + 12W^2 - 14W = 1680
W^3 + 6W^2 - 7W = 840
W^3 + 6W^2 - 7W - 840 = 0
Let f(w) = W^3 + 6W^2 - 7W - 840
The root of the polynomial occurs when f(w) = 0
So by trial and error let w = 8
Then we have 8^3 + 6(8)^2 - 7(8) - 840 = 0
Hence w = 8 is a root of the equation.
So we divide our polynomial by the root to obtain other roots, I.e W^3 + 6W^2
- 7W - 840 divide by w- 8. Doing this we have w = 15 and W = 14.
Hence the dimensions of the box is 8 * 15 * 14