178 is your budget deficit
700 - 522 = 178
100 feet in inches is 1200 inches, and 24 3/8 as an improper fraction is 195/8.
Divide 1200 by 195/8, or 1200/1 x 8/195.
1200/1 x 8/195 simplifies to 80/1 x 8/13, which equals 640/13. 640/13 equals about 49.23. So Carl can cut 49 FULL pieces.