SOLUTION: Use two equations in two variables to solve the problem. The perimeter of the rectangular garden shown below is 80 meters. The width of the garden is two-thirds its length, find

Algebra ->  Equations -> SOLUTION: Use two equations in two variables to solve the problem. The perimeter of the rectangular garden shown below is 80 meters. The width of the garden is two-thirds its length, find      Log On


   

Question 1162001: Use two equations in two variables to solve the problem.
The perimeter of the rectangular garden shown below is 80 meters. The width of the garden is two-thirds its length, find its area A.
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
.

These equations are


    2x + 2y = 80           (1)

     y = %282%2F3%29%2Ax,           (2)


where x is the length and y is the width of the garden.


From equation (2), you have  

    3y = 2x.                (3)


In equation (1), replace 2x by 3y, based on (3).  You will get then

   3y + 2y = 80

   5y      = 80

    y      = 80/5 = 16.


So, the width is 16 meters.


Then the length is  %2880-2%2A16%29%2F2 = 48%2F2 = 24 meters.


ANSWER.  The length is 24 m;  the width is  16 m.


CHECK.   16 m, the width, really is  2%2F3  of 24 m.

Solved.

The method I used in the solution, was a kind of the Substitution method.


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Comment from student: Thank you! i was able to figure out the rest of it to find the area. thanks a bunch!
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My response : I am glad to hear it (!)