Question 146063
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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Do this in thousands of dollars to avoid all those zero's
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Let x = no. of members currently in the club
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Cost per member {{{200/x}}}
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Original cost = Cost with 5 more + 2
{{{200/x}}} = {{{200/((x+5))}}} + 2
Multiply equation x(x+5) to get rid of the denominators
200(x+5) = 200x + 2x(x+5)
:
200x + 1000 = 200x + 2x^2 + 10x
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Arrange on the left as a quadratic equation:
2x^2 + 10x + 200x - 200x - 1000 = 0
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2x^2 + 10x - 1000 = 0
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Simplify
x^2 + 5x - 500 = 0
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Factor to:
(x+25)(x-20) = 0
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Positive solution:
x = 20 original members
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Check solution
Cost originally: 200/20 = 10k
Cost with 5 more: 200/25 = 8k