Polynomial word problem, given relationship between width and length

Question

I can not figure out how to solve this polynomial word problem, even when given the hint,

Write an equation using the difference: (area at first) - (area afterwards)

The question goes like this. There is a rectangle who is twice as wide as it is long. If you reduce its width by 10 ft and increase its length by 10 ft, that reduces the rectangle's area by 20 square ft. Find the original rectangle's width and length.

Answer 1

If we let $y$ be the area of the rectangle then we can set up a system of equations and solve it.

So if we let the width be $2x$ and the length be $x$ so putting this together we get $y=2x^2$.

Can you get another equation from what you have given us next? Then put them together!

Answer 2

Hint: To get started, draw a diagram and incrementally build it up with what the question tells you. This is a good way to start any geometry problem. You're given a rectangle, so draw the rectangle and label an unknown side-length $x$. You know that the rectangle is twice as wide as it is long, so label the rectangle's other sides accordingly. Consider what would happen to the side-lengths be if they were changed according to the question. How has the area changed? You can take it from here.