Question

A contractor charges $209 to carpet a 90-square-foot room and $289 to carpet a 140-square-foot room. the contractor charged a customer $553 to carpet a room under this same pricing plan. what was the area of the room that was carpeted?

Answer 1

90R + F = 209 
140R + F = 289 

If you solve this system of equations you get: 
R=$1.60/sq foot 
F=$65 

Let square footage to be carpeted be x 

1.6x + 65 = 553 
1.6x = 553-65 
x=(553-65)/1.6 
x=305 sq feet