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March 27, 2017

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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?

  • algebra repost - ,

    let x = the number of members currently in the club

    200,000/x = 200,000/(x+5) + 2000
    Multiply to eliminate fractions.
    200,000(x+5) = 200,000x + 2000(x)(x+5)
    200,000x + 1,000,000 = 200,000x + 2000x^2 + 10,000x
    1,000,000 = 2000x^2 + 10,000x
    2000x^2 + 10,000x - 1,000,000 = 0
    Divide by 2000.
    x^2 + 5x - 500 = 0
    (x+25)(x-20) = 0
    x = 20, -25

    The answer of x=-25 does not make sense in the context, so we are left with x=20 people.

  • algebra repost - ,

    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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