13 by 22 feet room 19.50 per square yard?

Convert the feet to yards first. (3 ft / linear yard - 9 Square Ft in a Sqr Yard)

13 feet = 4.25 yards
22 feet = 7.33 yards

4.25 yards x 7.33 yards = 31.2 square yards.

The price is (31.2 square yards) x ($19.50 per square yard) = $607.50

NOTE THAT

If you don't convert the feet to yards first, then divide the 'cost per yard' by 9 to get the 'cost per square foot' to avoid errors.