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What was the area of the room that was carpeted?

Algebra
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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?

Mar 20th, 2015

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

Mar 20th, 2015

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