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Math Help - system of inequalities

  1. #1
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    system of inequalities

    THe Quetion:

    The science club can spend at most $400 on a field trip to a dinosaur exhibit. It has enough chaperones to allow at most 100 students to go on the trip. The exhibit costs $3 for students 12 years and younger and $6 for students over 12.

    Problem:

    Write a system of linear ineqalities to model this situation.

    AND

    Graph your system of ineqalities. Be sure it is clear which region shows the solution.

    Thanks so much!!!

    Eeyore11
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  2. #2
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    Quote Originally Posted by eeyore11 View Post
    THe Quetion:

    The science club can spend at most $400 on a field trip to a dinosaur exhibit. It has enough chaperones to allow at most 100 students to go on the trip. The exhibit costs $3 for students 12 years and younger and $6 for students over 12.
    Let x variable represent the amount of younger students.
    Let y varialbe represent the amount of older students.

    Then, x+y <= 100

    Each x costs $3 thus in total 3x dollars.
    Each y costs $6 thus in total 6y dollars.
    The net total is, 3x+6y.
    Then, 3x+6y<=400

    This yields two inequalities,
    x+y<=100
    3x+6y<=400

    But there are two more, x>=0 and y>=0
    These are natural inequalities.
    Since you cannot have a negative amount of students going.

    So we really have,
    x+y<=100
    3x+6y<=400
    x>=0 and y>=0
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