SOLUTION: The Blumin Garden Club planned to give their president a gift of appreciation costing $120 and to divide the cost evenly. In the meantime, 5 members dropped out of the club. If it

Question 1157084: The Blumin Garden Club planned to give their president a gift of appreciation costing $120 and to divide the cost evenly. In the meantime, 5 members dropped out of the club. If it now costs each of the remaining members $2 more than originally planned, how many members initially participated in the gift buying?
Found 4 solutions by Boreal, ikleyn, josgarithmetic, mananth:
Answer by Boreal(15235)   (Show Source): You can put this solution on YOUR website!
they had x people who each gave 120/x dollars
now they have x-5 people who give 120/(x-5), and that is $2 more than the first
so 120/(x-5)=(120/x)+2=(120+2x)/x for common denominator. Cross-multiply
120x=(x-5)(120+2x)=120x+2x^2-600-10x
120x=120x_2x^2-10x-600, and the 120x on each side cancel
2x^2-10x-600=0
x^2-5x-300=0
(x-20)(x+15)=0
x=20, only positive value
20 people, each giving $6
now 15 people, each giving $8.
20 is the answer.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.

If n is the value under the question, then the equation to find n is THIS - = 2. Its solution is n = 20 (I solved the equation MENTALLY). You may deduce it to the standard quadratic equation form and solve formally.

Solved.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!

-

PRICE QUANTITY COST MEMBERS AS PLANNED 120/n n 120 FIVE FEWER MEMBERS 120/(n-5) n-5 120 DIFFERENCE 2

Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
let number of members be x
each member contributes 120/x
5 members leave
each contributes 120/(x-5)

2x^2-10x-600=0
x^2-5x -300 =0 ( divide by 2)
(x-20)(x+15)=0
x=20 OR -15 ignore negative
20 members originally.

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