Re: A rectangular solid is changed such that

Ok, so here is what I know:
~Old Volume = New Volume
~(L+1)(W+1)(H-9) = (L*W*H)
~(H-9) = 4w
~width, length of original rectangular are equal
So, from that I get:
(L+1)(W+1)(4w)=(W*W*H)
But in the book, the equation differs from mine in two ways.
For starters, mine is L+1)(W+1)(4w)=(W*W*H) while theirs is (W+1)(W+1)(4w)=(W*W*H)

If L=W then substitute L with W in the equation and obtain
(W+1)(W+1)(4W)=(W*W*H)- the one in the book

But here is my (apparently incorrect) reasoning.
L=W in the old rectangle, so why plug "W" into the new rectangle volume?
if (H-9)=4w, then why do I plug 4w into the new rectangle volume and h=4w-9 into the old rectangle formula? It seems unnecessary to have to plug in 4w for (h-9) then derive h=4w-9 and plug in on the other side.

You have
(W+1)(W+1)(H-9)=(W*W*H) and in order to solve it you need to express H in terms of W, so from H-9=4w you get H=4W+9 and H-9=4W
(W+1)(W+1)(4W)=(W*W*(4W+9))

The above equation is in W and H, so have to express all the variables in one term (W) in order to solve it. You have to plug in those values at both sides in order to solve the equation.

Hope it's clear, let me know