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Math Help - Word Problem. Can't figure out equation.

  1. #1
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    Word Problem. Can't figure out equation.

    Need help figuring out the equation you'd get from the following paragraph...

    A Broadway performance of The Phantom of the Opera had a paid attendance of 320 people. Balcony tickets cost 42$, and orchestra tickets cost 64$. Ticket sales receipts totaled 16,630$. How many tickets of each type were sold?

    I seem to have forgotten how I'd write this as an equation... I don't want to have the equation solved (yet, I'll see if I can get it on my own) but I've spent the last 20 minutes trying to find a way to make equations to help figure it out. I have to use a system of two linear equations to solve it, either addition method or substitution method.

    Thank you for any help.
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  2. #2
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    Talking

    Quote Originally Posted by complicated View Post
    A Broadway performance of The Phantom of the Opera had a paid attendance of 320 people. Balcony tickets cost 42$, and orchestra tickets cost 64$. Ticket sales receipts totaled 16,630$. How many tickets of each type were sold?
    Try an online lesson to learn the general set-up for "mixture" word problems.

    Once you've studied that, the following should make sense:

    . . .tickets:
    . . . . .total: 320
    . . . . .balcony: b
    . . . . .orchestra: 320 - b

    . . .income:
    . . . . .total: 16630
    . . . . .balcony: 42b
    . . . . .orchestra: ...

    Complete the table. Add the incomes from the two types of tickets, and set equal to the given total income. Solve for the variable.
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  3. #3
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    Quote Originally Posted by stapel View Post
    Try an online lesson to learn the general set-up for "mixture" word problems.

    Once you've studied that, the following should make sense:

    . . .tickets:
    . . . . .total: 320
    . . . . .balcony: b
    . . . . .orchestra: 320 - b

    . . .income:
    . . . . .total: 16630
    . . . . .balcony: 42b
    . . . . .orchestra: ...

    Complete the table. Add the incomes from the two types of tickets, and set equal to the given total income. Solve for the variable.
    Orchestra would be 16630 - 42b right?

    But I don't know what b is and have no equation to figure out what b could be so I can't solve it this way, unless I'm just missing something. That site you linked to me didn't really help me understand it.

    Edit: Hang on I might be getting it. bbiab
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  4. #4
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    Does this look right?

    let a = orchestra tickets sold
    let b = balcony tickets sold

    Tickets | $Tickets | Total
    320 - a | $42 | $42(320 - a) - balcony
    a | $64 | $64a - orchestra
    320 | --------| 16630 - total
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  5. #5
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    Lost again.

    Managed to get this much...

    42(320 - a) + 64a = 16630
    13440 - 42a + 64a = 16630
    13440 + 22a = 16630
    22a = 3190
    /22 = /22
    a = 145


    Where do I go from here though?

    Edit:

    Would I just take 320 - 145 = b?
    That seems too easy to me but makes sense, any feedback is appreciated.
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  6. #6
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    Yup. You've got it. To check your work, just make sure that

    a + b = 320
    and
    42(320-a) + 64(a) = 16630

    if a = 145, and b = 320-145 = 175
    then 145 + 175 = 320
    and
    42(175) + 64(145) = 7350 + 9280 = 16630
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