SOLUTION: A group of people could rent a social hall for $480. When 14 more people join the venture, the cost per person is decreased by $14. How many total people are in the group? (Hi

Question 80202: A group of people could rent a social hall for $480. When 14 more people join the venture, the cost per person is decreased by $14. How many total people are in the group?
(Hint: Let X + 14 equal the total number of people in the group)
I do not understand how to set this up. If you could please help, Thank you.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A group of people could rent a social hall for $480. When 14 more people join the venture, the cost per person is decreased by $14. How many total people are in the group?
-------------
Original Group DATA:
Let number of people be "x".
Cost per person for social hall = 480/x dollars
---------------------
New Group DATA:
Number of people is "x+14"
New cost per person = 480/(x+14)
------------------
EQUATION:
original cost per person - new cost per person = 14 dollars
480/x - 480/(x+14) = 14
Multiply thru by x(x+14) to get:
480(x+14) - 480x = 14x(x+14)
480x+14*480 -480x = 14x^2+(14^2)x
14*480 = 14x^2+(14^2)x
480 = x^2+14x
x^2+14x-480=0
(x-60)(x+8)=0
Positive answer:
x=60 (original size of the group)
x+14 (new size of the group)
==============
Cheers,
Stan H.

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