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anonymous

  • 5 years ago

The manager of a movie theatre wants to know the number of adults and children who go to the movies. The theatre charges $8.00 for each adult ticker and $4.00 for each child ticket. At a showing where 200 tickets were sold, the theatre collected $1,304. A) Write a system of equations to represent this situation. B) How many adult tickets and how many child tickets were sold? C) If the operating costs totaled $946.00, what is the amount of profit or loss per ticket?

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  1. anonymous
    • 5 years ago
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    let a = the number of adult tickets sold let c = the number of children tickets sold

  2. anonymous
    • 5 years ago
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    so we know there were 200 sold so..... a + c = 200

  3. anonymous
    • 5 years ago
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    What does our next equation have to do with? (the first one was about how many people attended)

  4. anonymous
    • 5 years ago
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    the next equation needs to deal with the profits being made... right?

  5. anonymous
    • 5 years ago
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    Good. each adult ticket cost 8.00 and each child cost 4.00 for a total of $1,304 so 8a + 4c = 1304

  6. anonymous
    • 5 years ago
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    then solve for each?

  7. anonymous
    • 5 years ago
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    a + c = 200 8a + 4c = 1304 do you know how to solve this system?

  8. anonymous
    • 5 years ago
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    9a + 5c = 1504?

  9. anonymous
    • 5 years ago
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    The way you do this is to do something to one of the equations to GET RID of one of the variables. I am going to get rid of the a's... so I will need to multiply the first equation by -8 so it cancels with the +8a in the 2nd equation

  10. anonymous
    • 5 years ago
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    -8(a + c = 200) 8a + 4c = 1304 -8a - 8c = -1600 8a + 4c = 1304 now add these

  11. anonymous
    • 5 years ago
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    -4c = -296?

  12. anonymous
    • 5 years ago
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    which means that c = 74?

  13. anonymous
    • 5 years ago
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    Yes... so substitute in a + c = 200 a + 74 = 200 a = 126

  14. anonymous
    • 5 years ago
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    Then part c. They made $1304 by selling tickets. It cost them $946 for movie rights, lights,etc. so they actually made $1304 - $946 = $358 They sold 200 tickets so they made $358/200 per ticket which is $1.79 per ticket.

  15. anonymous
    • 5 years ago
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    thank you soooooo much! i haven't had to do these since middle school and i've pretty much forgotten how, obviously. /:

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