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?