SOLUTION: the length and width of a rectangle are in the ratio 3:2. if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1. find t
Algebra.Com
Question 150507: the length and width of a rectangle are in the ratio 3:2. if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1. find the length and width of this rectangle.
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
the length and width of a rectangle are in the ratio 3:2. if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1. find the length and width of this rectangle.
.
Let x = length
and y = width
.
since we have two unknowns, we need two equations.
.
From: "the length and width of a rectangle are in the ratio 3:2." we get equation 1:
x/y = 3/2
or
2x = 3y (equation 1)
.
From: "if the length is increased by 20 and the width is decreased by 5, the ratio of the length to the width becomes 2:1" we get equation 2:
(x+20)/(y-5) = 2/1
or
(x+20) = 2(y-5) (equation 2)
.
Let's solve equation 1 for x:
2x = 3y
x = (3/2)y
.
Substitute the above into equation 2 and solve for y:
(x+20) = 2(y-5)
((3/2)y+20) = 2(y-5)
multiplying both sides by 2:
(3y+40) = 4(y-5)
3y + 40 = 4y - 20
60 = y
.
Finally, substitute the above into equation 1 and solve for x:
2x = 3y
2x = 3(60)
2x = 180
x = 90
.
length = 90
width = 60
RELATED QUESTIONS
The lenght and width of a rectangle are in the ratio 3:2. If the length is increased by... (answered by mangopeeler07)
the length and the width of a rectangle are in the ratio 3:2. if the length is increased... (answered by AAfter.Com)
If the length of a rectangle is increased by 40% and its width is decreased by 20%, what... (answered by checkley77)
if the length of a rectangle is increased by 20% and the width is decreased by 20%then... (answered by ankor@dixie-net.com)
if the length of a rectangle is increased by 20% and width of the same rectangle is... (answered by josgarithmetic)
if the length of a rectangle is increased by 30% and the width is decreased by 20%, then... (answered by ankor@dixie-net.com)
If the length of a rectangle is increased by 30%and the width is decreased by 20%,then... (answered by Alan3354)
if the length of a rectangle is increased by 120%and its width is decreased by 20%,what... (answered by nerdybill)
The lenght and the width of a rectangle are in the ratio 3:2. If the lenght is increased... (answered by Fombitz)