A hotel charges $20 for the use of its dining room and $2.50 a plate for each dinner. an association gives a dinner and charges $3 a plate but invites for non paying guests. if each person has one plate, how many paying persons must attend for the association to collect the exact amount to pay the hotel?

Answer: 64 paying persons must attend for the association to collect the exact amount to pay the hotel.

Step-by-step 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

40

Step-by-step explanation:

20 + 2.5x = 3x

20 = 0.5x

x = 40