Suppose that you want to carpet a rectangular room that is 6 feet by 12 feet. carpet costs $10 per square yard. note that 1 yard is 3 feet. how much does it cost to carpet the room

3 ft = 1 yd

so we have

6 ft = 2 yd . . . . . multiply the above equation by 2

12 ft = 4 yd . . . . multiply the previous equation by 2

The dimensions of the room are 2 yd by 4 yd, so the area is

... A = W×L = (2 yd)×(4 yd) = 8 yd²

The cost is $10/yd², so we multiply this figure by the number of yd² to get the total cost.

... cost = ($10/yd²)×(8 yd²) = $80

It will cost $80 to carpet the room.

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents