Question 792847: A banquet hall charges $100 for the use of its dining room and $7.50 a plate for each dinner. The civic club hosts a dinner party at the banquet hall and charges $10.00 a plate, but also invites ten nonpaying guests. If each person orders one plate, how many paying persons must attend for the civic club to collect the amount needed to pay the total cost of the dinner exactly?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A banquet hall charges $100 for the use of its dining room and $7.50 a plate for each dinner.
The civic club hosts a dinner party at the banquet hall and charges $10.00 a plate, but also invites ten nonpaying guests.
If each person orders one plate, how many paying persons must attend for the civic club to collect the amount needed to pay the total cost of the dinner exactly?
:
Let x = no. 0f paying guests
Then
(x+10) = total number of guests
:
10x = 7.50(x+10) + 100
10x = 7.50x + 75 + 100
10x - 7.5x = 175
2.5x = 175
x = 175/2.5
x = 70 paying people required
:
:
See if that works out,
amt paid = 70*10 = $700
total cost: 80*7.5 + 100 = 700
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