Every member of a certain club volunteers to contribute equally to the purchase of a $60 gift certificate. How many members does the club have?
(1) Each member's contribution is to be $4.
(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2.
The problem states that each member contributes equally to the gift certificate. Let the number of people be n and the amount contributed by each member be x. Now, from the question we know that total amount contributed=$60.
1) This statement tells us that contribution of each member=$4. i.e x=4
2) This tells us that if 5 members fail to contribute every person's contribution share increases by $2.
We know n=60/x
Now, new contribution=old contribution+2
i.e 60/(n-5)=2+ (60/n)
Bolded terms get cancelled
What remains is 2n^2-10n-300.
Take out 2
Factorize 150, you get 5*3*2*5
Take out common factors
n=-15 or 10. Since, the number of people cannot be negative it has to be 15.
Let me know if I can clarify something else.
how can you get the n=15.
you have to solve the equation.
and this is time consuming?
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