A rectangular lawn measures 7m by 5m. A uniform border of flowers is to be planted along two adjacent sides of the lawn. If the flowers that have been purchased will cover an area of 6.25 m^2, how wide is the border?

There might be more than 1 way to solve this, but here's what I come up with:

The lawn with flowers looks something like this:




7
------------------------------------
| X | FLOWERS |
|----|------------------------------|
| | |
| | | 5
| F | LAWN |
| | |
| | |
------------------------------------



So the area of the top row = 7 * X

The area of the side row = 5 * X

However, they overlap, and the part that overlaps = X * X , and it has to be subtracted from your total because otherwise it will be counted twice.

So your original equation is: (7X) + (5X) - (X^2) = 6.25


Combine: 12X - X^2 = 6.25

Then subtract from 1 side and put everything on the other. I like making the X^2 positive, so I add that to both sides and subtract 12X from both sides. That gives me:

0 = X^2 - 12X + 6.25

Then graph and solve.

I got 11.45 and 0.546. Only one of those is the answer.

If you plug those numbers back in, 11.45 doesn't work because 7 * 11.45 plus 5 * 11.45 = too big.

But 0.546 works.

0.546 * 7 + 0.546 * 5 = 6.552

Then subtract .55 * .55 = 6.25-ish