SOLUTION: The members of the theatre club were assessed equally to raise $400 for the purchase of new costumes. When four more people joined the club, the per member assessment was reduced b

Question 950250: The members of the theatre club were assessed equally to raise $400 for the purchase of new costumes. When four more people joined the club, the per member assessment was reduced by $5.00. What was the size of the club?
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
x=original members; a=original assessment;
ax=$400
x=$400/a
(x+4)(a-$5)=$400 Set equations equal.
(x+4)(a-$5)=ax Multiply.
ax+4a-$5x-$20=ax Subtract ax from each side.
4a-$5x=$20 Substitute for x
4a-$5($400/a)=$20
4a-$2000/a=$20 Subtract 4a from each side
-$2000/a=$20-4a Multiply each side by a
-$2000=$20a-4a^2 Add 2000 to each side
0=-4a^2+20a+2000

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=32400 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -20, 25. Here's your graph:

a=$25 The original assessment was $25
x=$400/$25=16 There were originally 16 members.
CHECK
ax=(x+4)(a-$5)=$400
$25(16)=20($20)=$400
$400=$400=$400

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