Question

Each person attending a fund-raising party for a certain club was charged the same admission fee. How many people attended the party?(1) If the admission fee had been $0.75 less and 100 more people had attended, the club would have received the same amount in admission fees.(2) If the admission fee had been $1.50 more and 100 fewer people had attended, the club would have received the same amount in admission fees.

Answer 1

(1) 400

(2) 200

Explanation:

Revenue (R) = ticket cost (C) * Number of sold (x)

R= Cx--------------------------------------------------------------- (1)

R = (C-0.75) * (x+100)

Cx = Cx +100C-0.75x -75

0.75x-100C = -75-------------------------------------------------(2)

R = (C+1.50)* (x-100)

Cx = Cx -100C+1.5x-150

-1.5x+100C= -150-------------------------------------------------(3)

Solving equations (2)and (3) simultaneously:

0.75x-100C = -75

-1.5x+100C= -150

-0.75x = -225

x= 300

(1) x+100

= 300 +100

= 400 people

(2) x-100

= 300-100

=200