SOLUTION: Here is the question below. I need to define the variable for x and y, write the appropriate equations, and solve the equation by either substitution, addition, or graphically. We

Question 19784: Here is the question below. I need to define the variable for x and y, write the appropriate equations, and solve the equation by either substitution, addition, or graphically. We were given multiple word problems and I am down to the last five and this is one of them. THX!
- The perimeter of a rectangle is 112m. If the width were doubled and the length were increased by 23m, the perimeter would be 232m. What are the length and width of the rectangle?
Answer by xcentaur(357) (Show Source):
You can put this solution on YOUR website!

The perimeter of a rectangle is 112m. If the width were doubled and the length were increased by 23m, the perimeter would be 232m. What are the length and width of the rectangle?

let the length be x and the width be y
perimeter=2(x+y)=112 metres
2(x+y)=112
x+y=56....[1]

if the width were doubled,new width=2y
length were increased by 23 m, new length=(x+23)
new perimeter=2(2y+x+23)=(4y+2x+46)=232 metres
4y+2x+46=232
4y+2x=232-46
2x+4y=186
x+2y=93....[2]

Taking equations 1 and 2 together we get,
x+y=56
x+2y=93
subtract equation[1] from [2]
x+2y-(x+y)=93-56
x+2y-x-y=93-56
2y-y=37
y=37

x+y=56
x=56-y=56-37=19

x=19 metres,y=37 metres

Hope this helps,
Prabhat