SOLUTION: My sister needs me to help her with a problem but i have not done math in a long time so i need your help please, here is the question. Q. A rectangular swimming pool is 2m long

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Question 575426: My sister needs me to help her with a problem but i have not done math in a long time so i need your help please, here is the question.
Q. A rectangular swimming pool is 2m longer than it is wide. If the width is decreased by 3m, and the length is increased by 4m, the area remains the same as the original area. find the original dimensions of the pool.
A. 18x20
I have found the answer because it is a riddle worksheet with multiple answers, but i do not know how to solve the problem itself without plugging it in.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length = L
Let the width = W
given:
(1) +L+=+W+%2B+2+
(2) +%28+W+-+3+%29%2A%28+L+%2B+4+%29+=+W%2AL+
-----------------------
Substitute (1) into (2)
(2) +%28+W+-+3+%29%2A%28+W+%2B+2+%2B+4+%29+=+W%2A%28+W+%2B+2+%29++
(2) +%28+W+-+3+%29%2A%28+W+%2B+6+%29+=+W%5E2+%2B+2W+
(2) +W%5E2+-+3W+%2B+6W+-+18+=+W%5E2+%2B+2W+
(2) +3W+-+18+=+2W+
(2) +W+=+18+
(2) +W+=+18+
and, since
+L+=+W+%2B+2+
+L+=+18+%2B+2+
+L+=+20+
The original dimensions are 18x20 m2