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

Answer:

Let a = admission fee

Let n = number of people who attended the party

(1) If the admission fee had been $0.75 less and 100 more people attended, the club would have received the same amount in admission fees.

$an=(a -0.75)(n+100)$

$an =an-0.75n+100a-75$

$0.75n-100a =-75$     ...(1)

(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.

$an=(a+1.50)(n-100)$

$an= an+1.5n-100a-150$

$1.5n-100a= 150$   ......(2)

Subtracting (1) from (2) we get

$0.75n=225$

n = 300

And substituting n = 300 to get value of a;

$1.5(300)-100a= 150$

$450-100a=150$$-100a=-450+150$

$100a=300$

a = 3

Hence, $3 was admission fee and 300 people attended the party.