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

Algebra ->  Customizable Word Problem Solvers  -> Finance -> 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      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

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) About Me  (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
400%2F%28%28x-4%29%29 = 400%2Fx + 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