Final answer:
There are 0 gallons in the tank after applying and adding the given amounts.
Step-by-step explanation:
To find the number of gallons in the tank after applying and adding the given amounts, we start with the initial amount of 283 5/8 gallons and subtract the amount applied, which is 178 3/2 gallons. This gives us 283 5/8 - 178 3/2 = 283 5/8 - 356 4/8 = -72 7/8 gallons. Since negative gallons don't make sense in this context, we can conclude that there are 0 gallons in the tank after applying and adding the given amounts.