Carpet costs $16 a square foot. a rectangular floor is 16 feet long by 14 feet wide. how much would it cost to carpet the floor?

The area of the floor is (16-ft x 14-ft) = 224 square feet.

IF carpet cost $16 per square foot, THEN enough carpet
to cover that floor would cost

             (224) x ($16) = $3,584 ,

and PLUS, you'd need to buy 224 square feet of pad to lay down
under the carpet, and pay more to have the whole thing installed. 
That's an awful lot of money for a little dinky 12' x 14' bedroom !

Carpet does NOT cost $16 per square foot. 
It's more like $16 per square YARD (plus pad and installation).

9 square feet = 1 square yard.

The area of the bedroom is (224/9) =  24-8/9 square yards

At $16 per each of those, the carpet costs  (24-8/9) x ($16) = $398.22 .
Much more reasonable !

Bis the correct answer