SOLUTION: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. Wh

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. Wh      Log On


   

Question 194145: The perimeter of a rectangle is six times the width. If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches. What is the width?
P = 2l + 2w
160 = (2l + 4) +(2w +7) When I substitute, it is just a mess.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let P = perimeter, L=length, and W=width


Note: the lower case letter "l" looks very similar to the number 1. So I'm using an uppercase L. So I figured to use uppercase for all the variables.


Now let's get the translations down:

"The perimeter of a rectangle is six times the width" translates to P=6W

Also, "If the length were increased by 4 inches and the width were increased by 7 inches, then the perimeter would be 160 inches" translates to 160=2%28L%2B4%29%2B2%28W%2B7%29

Finally, this is not explicitly stated, but the formula for the perimeter of any rectangle is P+=+2L+%2B+2W


P+=+2L+%2B+2W Start with the given perimeter formula


6W+=+2L+%2B+2W Plug in P=6W


6W+-+2W+=+2L+ Subtract 2W from both sides


4W+=+2L+ Combine like terms.


2L+=+4W+ Rearrange the equation


L+=+%284W%29%2F2+ Divide both sides by 2 to isolate L


L+=+2W+ Reduce


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160=2%28L%2B4%29%2B2%28W%2B7%29 Move onto the second equation


160=2L%2B8%2B2W%2B14 Distribute


160=2L%2B2W%2B22 Combine like terms.


160=2%282W%29%2B2W%2B22 Plug in L+=+2W+


160=4W%2B2W%2B22 Multiply


160=6W%2B22 Combine like terms.


160-22=6W Subtract 22 from both sides.


138=6W Combine like terms.


138%2F6=W Divide both sides by 6 to isolate W


23=W Reduce


So the width is W=23


L=2W Go back to the previously isolated formula


L=2%2823%29 Plug in W=23


L=46 Multiply


So the length is L=46


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Answer:

So the width is 23 inches and the length is 46 inches.