The length of a rectangle is 5 cm longer than twice the length of the width. if the are of the rectangle is 403 square centimeters, what is the width?

You could set up a system of equations and solve for that, and you 2 equations that you would use would be:
x=2y+5
xy=403
(x = length)
(y = width)
But for this problem, we can notice that:
we need 2 numbers that will multiply together and equal EXACTLY 403, and then they have to be in a somewhat similar range, because the larger number is only twice the smaller, plus a few. So, all we need to do is find 2 numbers that multiply to 403 that are within a few numbers. It turns out that the only two whole numbers that multiply to 403 are
31
and
13
Test them in either equation that is listed at the top, and they work. The question is asking for the width, and because the width doubled plus 5 equals the length, that means that the width will be the smaller number. Therefore, the width is 13 cm.