Question 24629
Let number of days the pattern runs be "x"
Each day the number of gumballs will be 1100-50x
The number of gumballs must be >= (20%)(1100)
INEQUALITY:
1100-50x >= (0.20)(1100)
1100-50x>= 220
    -50x>=-880
       x<=17.6 days
The company must change its filling pattern on the 
17th day because on the 18th day there will be fewer than
220 gumballs in the machine.

Cheers,
Stan H.