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Question 816271: [ members of the computer club were assessed equal amounts to raise $1200 to buy new software. When 8 [NEW] members joined, the per-member assessment was reduced by $7.50. What [IS] the new size of the club? ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! 1200 = (p - 7.50)(n + 8)
1200 = pn
p = 1200/n
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1200 = (p - 7.50)(n + 8)
1200 = pn + 8p - 7.50n - 60
1260 = pn + 8p - 7.50n
1260 = (1200/n)n + 8(1200/n) - 7.50n
1260 = 1200 + 9600/n - 7.50n
60 = 9600/n - 7.50n
60n = 9600 - 7.50nn
7.50n^2 + 60n - 9600 = 0
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the above quadratic equation is in standard form, with a=7.5, b=60, and c=-9600
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to solve the quadratic equation, plug this:
7.5 60 -9600
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
n = 32
n = -40
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the negative root doesn't make sense for the size of the club (number of members), so use the positive root
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Answer:
the old size of the club is 32 members
the new size of the club is 40 members
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the old per-member assessment was: 1200/32 = $37.50
the new per-member assessment is: 1200/40 = $30.00
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