SOLUTION: if the width of the rectangle is increased by 3, and the length by 5, the width becomes 3/4 of the length and the area is increased by 135 m^2. find the original dimensions.

Algebra ->  Rectangles -> SOLUTION: if the width of the rectangle is increased by 3, and the length by 5, the width becomes 3/4 of the length and the area is increased by 135 m^2. find the original dimensions.      Log On


   

Question 463439: if the width of the rectangle is increased by 3, and the length by 5, the width becomes 3/4 of the length and the area is increased by 135 m^2. find the original dimensions.
Answer by amoresroy(361) About Me  (Show Source):
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if the width of the rectangle is increased by 3, and the length by 5, the width becomes 3/4 of the length and the area is increased by 135 m^2. find the original dimensions.
Let x = the width
y = the length
===================================
1st equation:
x+3 = (3/4)(y+5)
Multiply both sides by 4/3 to get
4x/3+4 = y+5
y = 4x/3 - 1
==================================
2nd equation:
(x+3)(y+5) = xy + 135
xy+5x+3y+15 = xy + 135
5x+3y = 120
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Substitute y = 4x/3 -1 in 2nd equation to get
5x + 3(4x/3 -1) = 120
5x +4x -3 = 120
9x = 123
x = 13.67
y = 4(13.67)/3 - 1
y = 17.22
The original dimensions arwe 13.67 m and 17.22 m.