SOLUTION: The length of a certain rectangle is 8 more than the width. The perimeter of the rectangle is 6 more than five times the width. Find the width of the rectangle.

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Question 1188330: The length of a certain rectangle is 8 more than the width. The perimeter of the rectangle is 6 more than five times the width. Find the width of the rectangle.
Answer by ikleyn(52814) About Me  (Show Source):
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The length of a certain rectangle is 8 more than the width.
The perimeter of the rectangle is 6 more than five times the width.
Find the width of the rectangle.
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Let L be the length;  W be the width.


Then we have these two equations


    L - W = 8             (1)

    2L + 2W - 5W = 6      (2)


Simplify second equation; keep first equation as is


     L -  W = 8           (1')

    2L - 3W = 6           (2')


From equation (1'), express  L = W + 8 and substitute it in equation (2')


    2*(W + 8) - 3W = 6

    2W + 16   - 3W = 6

     16 - 6 - W = 0

      W         = 10

      L = W + 8 = 10 + 8 = 18.


ANSWER.  The length is 18 units.  The width is 10 units.

Solved.