SOLUTION: the blumin garden club planned to give their president a gift of appreciation costing $210 and to divide the cost evenly. in the mentime, 5 members dropped out of the club. if its

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Question 982770: the blumin garden club planned to give their president a gift of appreciation costing $210 and to divide the cost evenly. in the mentime, 5 members dropped out of the club. if its now cost each of the remanining member $2 more than originally planned, how many members initially participated in the gift buying? (hint if x= number in club initially 120/x= cost per member.)
Found 3 solutions by josgarithmetic, MathTherapy, stanbon:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
One of the costs must be wrong. Either 210 dollars OR 120 dollars. Here will stick with 210, but this could be put into another variable for better generality.

m, how many initial members participate
m-5, how many members after five dropout
PRICE initially, 210/m
NEW PRICE, 210%2Fm%2B2

Also the new price is 210%2F%28m-5%29;

These NEW PRICES must be equal.
highlight%28210%2Fm%2B2=210%2F%28m-5%29%29 and what you do is to solve this for m.

What if you say the cost is the variable, c.
Then to solve for m,
highlight_green%28c%2Fm%2B2=c%2F%28m-5%29%29
m%28m-5%29%28c%2Fm%2B2%29=%28c%2F%28m-5%29%29%28m%28m-5%29%29
c%28m-5%29%2B2m%28m-5%29=cm
cm-5c%2B2m%5E2-10=cm
cm is shown added to both sides, so add -cm;
-5c%2B2m%5E2-10=0
2m%5E2=5c%2B10
m%5E2=%285c%2B10%29%2F2
m=sqrt%28%285c%2B10%29%2F2%29
m=sqrt%28%285c%2B10%29%2F2%29%28sqrt%282%29%2Fsqrt%282%29%29
m=%281%2F2%29sqrt%282%285c%2B10%29%29
highlight%28m=%281%2F2%29sqrt%2810c%2B20%29%29

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!
the blumin garden club planned to give their president a gift of appreciation costing $210 and to divide the cost evenly. in the mentime, 5 members dropped out of the club. if its now cost each of the remanining member $2 more than originally planned, how many members initially participated in the gift buying? (hint if x= number in club initially 120/x= cost per member.)
Cost of gift: $210

Cost per person: 120%2Fx, according to HINT!!

What is the cost of the gift? $210 or $120? Are you that carefree that you cannot enter the correct number so you can get a correct answer?

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
the blumin garden club planned to give their president a gift of appreciation costing $120 and to divide the cost evenly. in the mentime, 5 members dropped out of the club. if its now cost each of the remanining member $2 more than originally planned, how many members initially participated in the gift buying? (hint if x= number in club initially 120/x= cost per member.)
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new average - original average = $2
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120/(x-5) - 120/x = 2
1/(x-5) - 1/x = 1/60
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60(x) - 60(x-5) = x(x-5)
x^2-5x-300 = 0
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Positive solution:
x = 20 (original number in the club)
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Cheers,
Stan H.
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