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kaylamalik_xo

  • 2 years ago

Tickets for a school play cost $5 if you buy them early, and $7 if you buy them the day of the show. If 200 tickets are sold, and the total amount of money from ticket sales was $1340, how many tickets were purchased early? A. 170 tickets B. 30 tickets C. 100 tickets D. 124 tickets

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  1. dietrich_harmon
    • 2 years ago
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    C

  2. kaylamalik_xo
    • 2 years ago
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    @dietrich_harmon how? ;o

  3. geoffb
    • 2 years ago
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    No kidding.

  4. geoffb
    • 2 years ago
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    Let early tickets be \(x\). Since there are 200 total, late tickets must be \(200 - x\). You also know that the sum of all tickets is $1340. So: \[5x + 7(200-x) = 1340\] Does that make sense to you?

  5. kaylamalik_xo
    • 2 years ago
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    @geoffb So it really is C?

  6. geoffb
    • 2 years ago
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    Definitely not.

  7. kaylamalik_xo
    • 2 years ago
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    I thought so @geoffb. I thought it was A.

  8. geoffb
    • 2 years ago
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    Careful...

  9. geoffb
    • 2 years ago
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    Did you work out the formula above? Does it make sense how I got it and what it means?

  10. kaylamalik_xo
    • 2 years ago
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    So Id end up with 4x+1400=1340?

  11. geoffb
    • 2 years ago
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    No, not 4x.

  12. geoffb
    • 2 years ago
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    \[5x + 1400 - 7x = 1340\]

  13. kaylamalik_xo
    • 2 years ago
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    -2x+1400=1340

  14. geoffb
    • 2 years ago
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    Yes, good.

  15. kaylamalik_xo
    • 2 years ago
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    x=30

  16. geoffb
    • 2 years ago
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    Very good! So once you solve for x, a very important step is to go back and look at what you chose x to represent. In this case, we chose for it to represent tickets purchased early. If we had let it represent tickets purchased late, you would end up with x = 170, but the answer *wouldn't* be A, because it is looking for tickets purchased early, not late.

  17. geoffb
    • 2 years ago
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    Does that make sense?

  18. kaylamalik_xo
    • 2 years ago
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    OH so its B

  19. geoffb
    • 2 years ago
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    Yes, and you can test it if you want (I would if you were doing a test. 30 early tickets x $5 = $150 170 late tickets x $7 = $1190 Total ticket revenue = $1340

  20. kaylamalik_xo
    • 2 years ago
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    thanks @geoffb

  21. geoffb
    • 2 years ago
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    You're welcome! :)

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