Word problem using "x"

[1karebear]

The length of one side of a square is decreased by 2 meters and the length of an adjacent side is increased by 1 meter. In the resulting rectangle, the length is twice the width. How long was a side of the original square?

I really do not even know where to start but here is what I attempted:
x+x+x+x=x-2+x-2+x+1+x+1
4x=4x+2
I know this is wrong because there would be no solution 0 does not equal 2. My book states the answer is 5 meters, but I do not know how to reach that solution. Thank you in advance for any help provided!

Karrie

 

[kasie-tutor]

Dear Karrie (1karebear),

I really do not even know where to start but here is what I attempted:
x+x+x+x=x-2+x-2+x+1+x+1
4x=4x+2

In your expression above, you set the perimeter of the original square equal to the perimeter of the rectangle. It can't be assumed that these perimeters are equal unless they say that in the problem.

What you did get right is that the length of the rectangle is \(\displaystyle (x+1)\) and the width is \(\displaystyle (x-2)\).

How could you translate the part of the problem below? This is your clue about how to relate your lenght and width in an equation. Translate it just like it reads:

In the resulting rectangle, the length is twice the width.

The length (\(\displaystyle x+1\)) is (\(\displaystyle =\)) twice (\(\displaystyle 2\cdot\)) the width (\(\displaystyle x-2\)).

\(\displaystyle (x+1)=2(x-2)\).

Can you do it now?

 

[1karebear]

It makes so much sense!

I was trying to make it harder than it had to be.

x+1=2(x-2)
x+1=2x-4
1x-1x+1=2x-1x-4
1=1x-4
1+4=1x
x=5 meters

Thank you so much!

Karrie