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.

(1) 400

(2) 200

Step-by-step 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

f(x) = - 2/3x + 5; f(5/2)

substitute 5/2 in for x:

f(5/2) = -2/3(5/2) + 5

simplify the right side:

f(5/2) = -5/3 + 5

f(5/2) = 10/3

answer:

f(5/2) = 10/3

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