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?

Given only two points and expected to solve it, it;s fair to assume this is a system of linear equations, of the form Cost = Area * Price per square foot + Constant. Let's call the cost per square foot a, and the constant c: