Answer: 64 paying persons must attend for the association to collect the exact amount to pay the hotel.
Explanation:
Let x represent the number of paying guests that would attend the occasion.
The hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. This means that the total charge for x paying guests would be
2.5x + 20
The association gives a dinner and charges $3 a plate but invites four non paying guests. If each one has a plate and 4 guests are not paying, then the revenue that can be generated would be
3(x - 4)
For the association to collect the exact amount to pay the hotel, the number of paying persons that must attend would be
2.5x + 20 = 3(x - 4)
2.5x + 20 = 3x - 12
3x - 2.5 = 20 + 12
0.5x = 32
x = 32/0.5
x = 64