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Math Help - Quadratic Worded Problem. HELP.

  1. #1
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    Exclamation Quadratic Worded Problem. HELP.

    How do you work this out?

    Tickets for a concert are available at two prices. The more expensive ticket is $30 more
    than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the
    cheaper tickets than the expensive ones for $1800.
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  2. #2
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    Quote Originally Posted by amanda.chonghalliday View Post
    How do you work this out?

    Tickets for a concert are available at two prices. The more expensive ticket is $30 more
    than the cheaper one. Find the cost of each type of ticket if a group can buy 10 more of the
    cheaper tickets than the expensive ones for $1800.
    An approach:

    Let X = cost of expensive ticket, Y = cost of cheap ticket, n = number of expensive tickets that can be bought for $1800.

    Then:

    X = Y + 30 .... (1)

    nX = 1800 .... (2)

    (n + 10)Y = 1800 => nY + 10Y = 1800 .... (3)

    Sub (1) into (2): n(Y + 30) = 1800

    Expand: nY + 30n = 1800 .... (4)

    (4) - (3) => Y = 3n. Sub this into (3):

    (n + 10)(3n) = 1800 \Rightarrow 3n^2 + 30n - 1800 = 0 \Rightarrow n^2 + 10n - 600 = 0 \Rightarrow n = 20 (the negative solution is discarded since n > 0).

    Sub n = 20 into (2): X = 90.

    Sub X = 90 into (1): Y = 60.

    Also answered here: http://www.mathhelpforum.com/math-he...-problems.html.

    Thread closed.
    Last edited by mr fantastic; March 21st 2009 at 11:27 PM.
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