SOLUTION: The members of a computer club were to be assessed equally to raise $400 for the purchase of software. When four more persons joined the club, the per-member assessment was reduced

Question 168056This question is from textbook Algebra and Trigonometry
: The members of a computer club were to be assessed equally to raise $400 for the purchase of software. When four more persons joined the club, the per-member assessment was reduced by $5.00. What was the new size of the club membership? This question is from textbook Algebra and Trigonometry

Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The members of a computer club were to be assessed equally to raise $400 for the
purchase of software. When four more persons joined the club, the per-member
assessment was reduced by $5.00. What was the new size of the club membership?
:
Let x = new size club membership
then
(x-4) = original club membership
:
Original cost per member = New cost per member + $5
= + 5
:
Multiply equation by x(x-4) to get rid of the denominators, results:
400x = 400(x-4) + 5x(x-4)
:
400x = 400x - 1600 + 5x^2 - 20x
:
0 = 400x - 400x - 1600 + 5x^2 - 20x
:
A quadratic equation:
5x^2 - 20x - 1600 = 0
Simplify, divide equation by 5:
x^2 - 4x - 320 = 0
Factor to:
(x - 20)(x + 16) = 0
Positive solution is what we want here:
x = 20 new members
:
:
Check solution by finding the cost per person
400/16 = $25
400/20 = $20
------------
differ = $5

RELATED QUESTIONS
Hello! Can somebody help please? The members of a computer club were to be assessed (answered by stanbon)

The members of the theatre club were assessed equally to raise $400 for the purchase of... (answered by macston)

Members of the Computer Club were assessed equal amounts to raise $1200 to buy some... (answered by Paul)

[ members of the computer club were assessed equal amounts to raise $1200 to buy new... (answered by TimothyLamb)

Members of a boating club were assessed equally to raise $600 to pay for a new set of... (answered by josgarithmetic,MathTherapy)

Members of the Math Club were assessed equal amounts to raise $900 to buy graphing... (answered by richwmiller,MathTherapy)

Question: Members of the computer club were assessed equal amounts to raise $1200 to buy (answered by scott8148)

Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6... (answered by stanbon)

Members of the Ski Club contributed equally to obtain $1800 for a holiday trip. When 6... (answered by checkley71)