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.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
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.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
312 \text{ dollars}
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.
train