Question 174609: Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club?
Found 2 solutions by checkley77, stanbon:
Answer by checkley77(12844)   (Show Source):
You can put this solution on YOUR website! 200,000/x-200,000/(x+5)=2,000
(200,000[x+5]-200,000x)/x(x+5)=2,000
(200,000X+1,000,000-200,000X)/X^2+5X=2,000
1,000,000/(X^2+5X)=2,000
2,000X^2+10,000X=1,000,000
2,000X^2+10,000X-1,000,000=0
2,000(X^2+5X-500)=0
2,000(X+25)(X-20)=0
X-20=0
X=20 IS THE NUMBBER OF ORIGINAL MEMBERS.
pROOF:
200,000/20-200,000/25=2,000
10,000-8,000=2,000
2,000=2,000
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Sharing cost. The members of a flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club?
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Let original # in the club be "x"; average share = 200,000/x dollars
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After finding 5 more members "x+5"; average share = 200,000/(x+5) dollars
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Equation:
original average - new average = 2000
200,000/x - 200,000/(x+5) = 2000
Divide thru by 2000 to get:
100/x - 100/(x+5) = 1
100(x+5) - 100x = x^2+5x
500 = x^2+5x
x^2 + 5x -500 = 0
(x-20)(x+25) = 0
x = 20 (original # of members
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Ceers,
Stan H.
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