Algebra equation

Question

The dimensions of a rectangle are such that its length is 7 inches more than its width, if the length were doubled, and if the width were decreased by 3 inches the are would be increased by 198in^2. What are the length and width?

Answer 1

let x=Length, y= width

x=7+y

Area

=xy=7y+y^2

double Length, decrease width by 3

2x(y-3)=(14+2y)(y-3)=2y^2+8y-42=new A= 198+7y+y^2

y^2+y-240=0 = (y+16)(y-15) ignore the negative solution

y-15=0

y=15 inches wide

x=y+7= 22 inches Long

check the answers

xy=330= old Area

44(12)=528= new Area

198+330=528