Question

Allie has a birthday present for her brother. The length of the box that the present comes in is two times longer than the width of the box. The height of the box is 5 inches and its volume is 160 cubic inches. What is the length and width of the box?

Answer 1

Start by recalling that the volume of a rectangle is:\[V=L*W*H\]The problem gives you two of those values so that becomes:\[160=L*W*5\]Which simplifies to\[32=L*W\]
The problem also states that the length of the box is twice it's width so L = 2W.
Plug that back in for L in the last equation and solve for W:\[32=2W*W=2W^2\]\[16=W^2\]\[\sqrt{16}=W=4\]So W = 4 inches...and since you know that L = 2W, L must be 8 inches.