### Instruction: The cost to carpet a floor is directly proportional to the area.  It costs $\$$105 to carpet a floor that is $14\times 5
$ square feet.  How much will it cost to carpet a floor that is $16\times 13$ square feet? Express your answer in dollars.### Response: I know that the cost per square foot is the same for both floors, since the cost is directly proportional to the area.
So I can find the cost per square foot by dividing the total cost by the area.
For the first floor, the cost per square foot is $\frac{105}{14\times 5}=\frac{105}{70}=\frac{3}{2}$ dollars per square foot.
For the second floor, the area is $16\times 13=208$ square feet.
To find the total cost, I can multiply the area by the cost per square foot.
The total cost is $208\times \frac{3}{2}=104\times 3=312$ dollars.