Hi thangvietnam,
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.
Hence, n*x=60
1) This statement tells us that contribution of each member=$4. i.e x=4
Hence, n=60/4=15
SUFFICIENT
2) This tells us that if 5 members fail to contribute every person's contribution share increases by $2.
We know n=60/x
old n=n
new n=n-5
Old contribution=60/n
new contribution=60/(n-5)
Now, new contribution=old contribution+2
i.e 60/(n-5)=2+ (60/n)
60/(n-5)=(2n+60)/n
Cross multiplying
60n=(2n+60)(n-5)
60n = 2n^2+
60n-10n-300
Bolded terms get cancelled
What remains is 2n^2-10n-300.
Take out 2
n^2-5n-150=0
Factorize 150, you get 5*3*2*5
15-10=5
Hence, n^2-15n+10n-150=0
Take out common factors
n(n-15)+10(n-15)=0
n=-15 or 10. Since, the number of people cannot be negative it has to be 15.
SUFFICIENT
Let me know if I can clarify something else.
thangvietnam wrote:
how can you get the n=15.
you have to solve the equation.
and this is time consuming?