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Math Help - Pricing concert tickets

  1. #1
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    Pricing concert tickets

    Tickets to a rock concert cost $4, and the projected attendance is 300 persons. It is further projected that for every 10 increase in ticket price, the average attendance will decrease by 5. At what ticket price will the nightly receipts be $1,248?
    I'm having difficulty setting this problem up. I've tried several attempts but none have been successful.
    Can someone break it down to me, please?
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  2. #2
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    Quote Originally Posted by Tazo View Post
    I'm having difficulty setting this problem up. I've tried several attempts but none have been successful.
    Can someone break it down to me, please?
    $4.00 * 300 guests = $1200
    $4.10 * 295 guests = $1209.50
    $4.20 * 290 guests = $1218

    In general,

    (4 + (.1 * x)) * (300 - (5 * x)) = gross reciepts. Do you see why?
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  3. #3
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    Wait, so you're basically saying:

    (4 + .1x)(300 - 5x) = 1248, Right?

    Well, I tried that and my answers come out to be $8 and $12.

    In the back of the book the answers are: $4.80 & $5.20.

    Um...am I missing something?
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  4. #4
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    Quote Originally Posted by Tazo View Post
    Wait, so you're basically saying:

    (4 + .1x)(300 - 5x) = 1248, Right?

    Well, I tried that and my answers come out to be $8 and $12.

    In the back of the book the answers are: $4.80 & $5.20.

    Um...am I missing something?
    you're right. You're answers are x = 8 and x = 12.

    When x = 8, the equation looks like

    (4 + .1(8))(300 - 5(8) = 1248
    (4 + .8)(300 - 40 = 1248
    $4.80 * 260 = 1248

    See now?
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