Each person attending a party was charged the same admission

[Luci]

Each person attending a party was charged the same admission fee. How many people attended the party?

1- If the fee had been 0.75$ less and 100 more people had attended, the club would have made the same amount of money.
2- If the fee had been 1.50$ more and 100 fewer people had attended, the club would have made the same amount of money.

The answer is C) both statements, but how do we put it algebraically?

Thanks

[GMAT 2007]

Lets assume, the fee be x/person and the no. of people attended be y

from (1) Total money the club made = (x- 0.75)(y+100)
from (2) ....................................... = (x+1.50)(y-100)

from (1) & (2)

(x-3/4)(y+100) = (x+3/2)(y-100)

(4x-3)(y+100)/4 = (2x+3)(y-100)/2

4xy + 400x - 3y - 300 = 4xy-400x + 6y - 600

800x = 9y-300, we go two variables and one equation, can't solve. Are you sure the answer is (C)?

GMAT 2007

[Luci]

Yes, during the exam I did exactly what you have done and that is why I selected E),

but the GMATprep says its C.

Anyother idea?

Thnaks GMAT 2007

[GMAT 2007]

The part we missed is to use a common component xy in both the equations, if we use that than we will have two different equations with to variables to solve.

xy = (x-3/4)(y+100)...(1)
xy = (x+3/2)(y-100)...(2)


GMAT 2007