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Sophia.13

  • 3 years ago

A children's movie is playing at the local theater. The first showing earned $896 in ticket sales, and there were 56 adults and 112 children in attendance. The second showing earned $552 in ticket sales, and there were 23 adults and 92 children in attendance. find the price of an adult's ticket and the price of a child's ticket. A. Adult: $8.50; Child: $6.25 B. Adult: $8.00; Child: $4.00 C. Adult: $7.00; Child: $6.00 D. Adult: $7.50; Child: $5.75

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  1. Dido525
    • 3 years ago
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    Do you realize you have to make a system of equations?

  2. Dido525
    • 3 years ago
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    @Sophia.13

  3. Dido525
    • 3 years ago
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    You there? :P .

  4. Sophia.13
    • 3 years ago
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    Sorry, yeah I'm here and no.. i dont know what to do at all. /:

  5. Dido525
    • 3 years ago
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    Okay you have two situations, whenever you have 2 situations you usually have to make a system of equations.

  6. Dido525
    • 3 years ago
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    First of all do you KNOW what a system of equations is?

  7. Sophia.13
    • 3 years ago
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    Okay, and no..

  8. Dido525
    • 3 years ago
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    It's where you work with two equations and different variables.

  9. Dido525
    • 3 years ago
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    For example like: |dw:1356304863230:dw|

  10. Sophia.13
    • 3 years ago
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    ohh ok

  11. Dido525
    • 3 years ago
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    Do you understand?

  12. Sophia.13
    • 3 years ago
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    kinda

  13. Dido525
    • 3 years ago
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    The idea for a system of equations is to solve for both of the variables.

  14. Sophia.13
    • 3 years ago
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    ohh okkay i get it

  15. Dido525
    • 3 years ago
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    So I said: |dw:1356304949957:dw|

  16. Dido525
    • 3 years ago
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    Since you are just learning this we will use substitution.

  17. Sophia.13
    • 3 years ago
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    ok

  18. Dido525
    • 3 years ago
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    BTW this is NOT the question. It's just an example.

  19. Dido525
    • 3 years ago
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    By substitution I mean that you make one variable in terms of another variable.

  20. Dido525
    • 3 years ago
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    Does that make sense?

  21. Sophia.13
    • 3 years ago
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    Yeah

  22. Dido525
    • 3 years ago
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    |dw:1356305047829:dw|

  23. Dido525
    • 3 years ago
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    Does that make sense?

  24. Sophia.13
    • 3 years ago
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    kiinda

  25. Dido525
    • 3 years ago
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    Okay, what is it you don't get? :)

  26. Sophia.13
    • 3 years ago
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    Its just a little confusing hah, but i think i it now.

  27. Dido525
    • 3 years ago
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    Are you sure? :) . I got time. I can explain if you really need to :) .

  28. Dido525
    • 3 years ago
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    Basically, I said that x=5-y from the first equation. Since I know x=5-y I substituted the x in the second equation with 5-y instead of an x.

  29. Dido525
    • 3 years ago
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    Does that make sense?

  30. Sophia.13
    • 3 years ago
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    Why dont u just use x instead of substituting it with y?

  31. Dido525
    • 3 years ago
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    The problem with that is that we don't know what x is equal to. So we have to get rid of that x somehow.

  32. Dido525
    • 3 years ago
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    From the first equation we are given x+y=5 . So x=5-y Since we know x=5-y we can substitute that for x in the second equation and solve for y. After solving for y we can solve for x easily afterwards.

  33. Dido525
    • 3 years ago
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    Does that make sense? :) .

  34. Sophia.13
    • 3 years ago
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    yeah, but i just dont understand why you need to substitute x with y instead of just keeping x, x?

  35. Dido525
    • 3 years ago
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    Okay, think of it this way. Do you know what x is equal to?

  36. Sophia.13
    • 3 years ago
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    no

  37. Dido525
    • 3 years ago
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    We aren't given any values for x at all.

  38. Sophia.13
    • 3 years ago
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    oh

  39. Dido525
    • 3 years ago
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    So how would you solve for x unless you get rid of it somehow? :) .

  40. Dido525
    • 3 years ago
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    Does that make sense?

  41. Sophia.13
    • 3 years ago
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    Oh i get it nowww

  42. Dido525
    • 3 years ago
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    Good! :D .

  43. Dido525
    • 3 years ago
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    Okay then. So we have: |dw:1356305797768:dw| |dw:1356305817320:dw|

  44. Dido525
    • 3 years ago
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    Wait wait!!! That's not the question!!! :P . I just provided an example.

  45. Dido525
    • 3 years ago
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    |dw:1356305892765:dw|

  46. Dido525
    • 3 years ago
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    @Sophia.13 : Now shall we work on your question together? :) .

  47. Sophia.13
    • 3 years ago
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    Okay.(:

  48. Dido525
    • 3 years ago
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    Let the children's ticket's price be x Let the adult's ticket's price be y.

  49. Dido525
    • 3 years ago
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    Do you get that?

  50. Sophia.13
    • 3 years ago
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    Yeah

  51. Dido525
    • 3 years ago
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    One second. Can you hold on? I need to actually do this out myself ^_^ .

  52. Dido525
    • 3 years ago
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    Ohh sorry let's switch that. Let the adult's ticket's price be x Let the children's ticket's price be y.

  53. Dido525
    • 3 years ago
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    Do you get that?

  54. Dido525
    • 3 years ago
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    We know that in the first opening the total earnings for the adults and children combined equaled $896 We also know that in the second opening the total earnings for the adults and children equaled $552.

  55. Dido525
    • 3 years ago
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    Does that make sense?

  56. Sophia.13
    • 3 years ago
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    yeah that makes sense

  57. Dido525
    • 3 years ago
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    In the first opening there were 56 adults and 112 children and the sum of both of those equaled 896 after they bought there tickets.

  58. Dido525
    • 3 years ago
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    So can you see a way to make an equation from that?

  59. Dido525
    • 3 years ago
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    Let the adult's ticket's price be x Let the children's ticket's price be y.

  60. Sophia.13
    • 3 years ago
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    56x + 112y = 896 ?

  61. Dido525
    • 3 years ago
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    Excellent job!

  62. Dido525
    • 3 years ago
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    Now in the second opening week, there were 23 adults and 92 kids and there tickets equaled a total of $552.

  63. Dido525
    • 3 years ago
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    Can you make an equation from that?

  64. Sophia.13
    • 3 years ago
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    23x + 92y = 552 ? c:

  65. Dido525
    • 3 years ago
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    Very good! :) .

  66. Dido525
    • 3 years ago
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    So we have: |dw:1356306963125:dw|

  67. Dido525
    • 3 years ago
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    Now, we don't what any of the prices are so we have to get rid of one of the variables.

  68. Dido525
    • 3 years ago
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    Do you understand? :) .

  69. Dido525
    • 3 years ago
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    Now, we don't know*

  70. Sophia.13
    • 3 years ago
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    Yeah i understand.

  71. Dido525
    • 3 years ago
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    Now let's pick the first equation. Can you solve for x? :) .

  72. Dido525
    • 3 years ago
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    Aww shucks. :P . Thanks for the fanning.

  73. Sophia.13
    • 3 years ago
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    No problem C:

  74. Dido525
    • 3 years ago
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    yes, there is going to be a bunch of ugly fractions involved.

  75. Sophia.13
    • 3 years ago
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    I dont exactly remember how to solve for x.. i swear my brain just went through a time warp and lost my mathematical memory -___-

  76. Dido525
    • 3 years ago
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    It's okay... :) . |dw:1356307195870:dw|

  77. Dido525
    • 3 years ago
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    Now what would you do? :) .

  78. Sophia.13
    • 3 years ago
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    Um..for 56x = 896-112y dive both sides of the equation by 56?

  79. Dido525
    • 3 years ago
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    yep :) .

  80. Dido525
    • 3 years ago
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    See? You remember just fine :) .

  81. Dido525
    • 3 years ago
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    So x equals...? :)

  82. Sophia.13
    • 3 years ago
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    Hah so x = 16 - 112y? i dont think thats right is it?

  83. Dido525
    • 3 years ago
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    No :3 . |dw:1356307670894:dw|

  84. Dido525
    • 3 years ago
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    I tend to avoid simplyfing. Don't ask why.

  85. Sophia.13
    • 3 years ago
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    Ohhhhh that makes sense. :P

  86. Dido525
    • 3 years ago
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    Now we know what x equals in terms of y.

  87. Dido525
    • 3 years ago
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    We have: |dw:1356307766229:dw|

  88. Dido525
    • 3 years ago
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    We know what x equals. Can you substitute for x? :) .

  89. Dido525
    • 3 years ago
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    Yes, there is an ugly fraction involved.

  90. Sophia.13
    • 3 years ago
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    I dont know what to do .-.

  91. Dido525
    • 3 years ago
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    Okay so we have:|dw:1356308102259:dw|

  92. Dido525
    • 3 years ago
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    We know x equals

  93. Dido525
    • 3 years ago
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    |dw:1356308121223:dw|

  94. Sophia.13
    • 3 years ago
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    hold on a sec please. I'll brb(:

  95. Dido525
    • 3 years ago
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    Substitute for x.

  96. Dido525
    • 3 years ago
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    Okay :) .

  97. Dido525
    • 3 years ago
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    |dw:1356308143795:dw|

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