SOLUTION: The area of a rectangular wall in a classroom is 171 square feet. Its length is 8 feet shorter than three times its width. Find the length and width of the wall of the classroom.

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Question 1111376: The area of a rectangular wall in a classroom is 171 square feet. Its length is 8 feet shorter than three times its width. Find the length and width of the wall of the classroom.
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
system%28xy=171%2Cx=3y-8%29

y%283y-8%29=171
3y%5E2-8y=171
3y%5E2-8y-171=0
%283y%2B19%29%28y-9%29=0---------------highlight_green%28y=9%29 makes sense here...
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Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Algebra doesn't really help you with this problem. If you take the path suggested by the other tutor, you end up having to try to solve the equation
3y%5E2-8y-171+=+0, presumably by factoring. To do that, part of what you need to do is find two numbers whose product is 171; then you have more work to do after that.

You can reach the answer much faster simply by starting with the fact that the product of the length and width is 171 and finding which two integers with a product of 171 satisfy the other conditions of the problem.

171 = 1*171
171 = 3*57
171 = 9*19

Only the last of these works: 19 is 8 less than 3 times 9.

So the width is 9 feet and the length is 19 feet.