Purchased 297 square feet of carpet at $18.50 a square yard, what is the cost?

297 / 9 = 33 yards X $18.50 =$610.50
Do I divide by 3 again to get $203.50?

no, why would you divide by 3?

you correctly converted the square feet to square yards by dividing by 9, and your cost was in square yards.

your cost is $610.50