Description
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?
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Explanation & Answer
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:
90a + c = 209
140a + c = 289
Subtract the first from the second:
50a = 80
a = 1.6
Sub that back in to find c:
90*1.6 + c = 209
144 + c = 209
c = 65
So now we have:
Area * 1.6 + 65 = cost
And for cost 553 we get:
1.6A + 65 = 553
1.6A = 488
A = 305 square feet
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