Math

For the first of two basketball games the price of each reserved seat was $1.50,the price of each unreserved seat was 5 cents, and the number of reserved seats sold was 1/25 of the number of unreserved seats sold.If, at a second game, the price of the reserved seats is to be reduced to $1.00,what proportion should be reserved to give the same receipts, provided the same number of seats are sold?

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asked by Lina
  1. If there are x reserved seats, receipts were

    1.50x + .05*25x = 2.75x
    Now, we want y reserved $1 seats to fetch the same money:

    1.00y + .05(26x-y) = 2.75x

    y + 1.3x - .05y = 2.75x
    .95y = 1.45x
    y/x = 1.45/.95 = .29/.19 = 29/19

    So, now we want y/26x = 29/494

    The ratio of reserved to unreserved is thus 29/465

    Check:
    If there are 494 seats, there were originally

    19 @ 1.50 = 28.50
    475 @ .05 = 23.75
    total: 52.25

    Now, there are
    29 @ 1.00 = 29.00
    465 @ .05 = 23.25
    total: 52.25

    Naturally, any multiples of 494 will also work.

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    posted by Steve

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