SOLUTION: In a math society the members were discussing how to divide the cost of their $3120 bill. It was agreed that each member should pay an equal amount. However 4 members resigned le

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Question 802025: In a math society the members were discussing how to divide the cost of their $3120 bill. It was agreed that each member should pay an equal amount. However 4 members resigned leaving remaining members to pay an extra $26 each. How many members did the society originally have?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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In a math society the members were discussing how to divide the cost of their $3120 bill.
It was agreed that each member should pay an equal amount.
However 4 members resigned leaving remaining members to pay an extra $26 each.
How many members did the society originally have?
:
Let x = no. of original members
then
(x-4) = actual no. of members that paid
:
3120%2Fx = original cost for each member
and
3120%2F%28%28x-4%29%29 = actual amt each had to pay
:
The equation:
3120%2F%28%28x-4%29%29 - 3120%2Fx = 26
multiply by x(x-4) resulting in
3120x - 3120(x-4) = 26x(x-4)
3120x - 3120x + 12480 = 26x^2 - 104x
A quadratic equation
0 = 26x^2 - 104x - 12480 = 0
Simplify, divide by 26
x^2 - 4x - 480 = 0
Factors to
(x-24)(x+20) = 0
The positive solution is all we want here
x = 24 original members
:
:
See if that checks out, find the actual cost for each scenario
3120/20 = $156
3120/24 = $130