SOLUTION: Please help!!!!!! 92) Sharing Cost. The members of a flying club plan to share equally the cost of a $ 2000,000 airplane. The members want to find five more people to join the c

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Question 126353: Please help!!!!!!
92) Sharing Cost. The members of a flying club plan to share equally the cost of a $ 2000,000 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 people are in the original group?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The members of a flying club plan to share equally the cost of a $ 2000,000 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 people are in the original group?
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I am going to assume you mean a $200,000 airplane
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Let x = no. of people in the original group
Then
(x+5) = no. of people that will reduce the cost per person by $2000
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Original cost - 2000 = with added people cost
200000%2Fx - 2000 = 200000%2F%28x%2B5%29
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Multiply equation by x(x+5) to get rid of the denominators, results:
20000(x+5) - 2000x(x+5) = 20000x
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20000x + 1000000 - 2000x^2 - 10000x = 200000x
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-2000x^2 + 200000x - 10000x - 200000x + 1000000 = 0
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-2000x^2 - 10000x + 1000000
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Let's divide the equation by -2000, this will change the signs & simplify it greatly
x^2 + 5x - 500 = 0
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This will factor to:
(x + 25)(x - 20) = 0
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The positive solution is what we want:
x = 20 people originally
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Check our solution:
200000%2F20 = $10000
200000%2F25 = $8000; confirms our solution
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How about this. Did it make sense to you. Not that hard, just a lot of zeros