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9 July, 11:53

Seventy people attended a concert. A general admission ticket is $4.75 and a student is $3.25. If the box office collected $272.50, how many general admissions and how many student tickets were sold.

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  1. 9 July, 12:10
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    Step-by-step explanation:

    Let g = amount of general admission tickets

    Let s = amount of student tickets

    Since seventy people attended the concert, this includes the people who bought general admission tickets and the people who bought the student tickets. As a result, g + s = 70. A student ticket is $3.25, so it would be 3.25s and a general admission ticket is $4.75, so it would be 4.75g. Since there was $272.50 collected in all, the second equation would be 3.25s + 4.75g = 272. 50.

    g + s = 70

    4.75g + 3.25s = 272.50

    Multiply the first equation by 3.25 (or 4.75) so that you can use elimination to get rid of one variable.

    3.25g + 3.25s = 227.50

    4.75g + 3.25s = 272.50

    Now, you subtract so that you can eliminate s.

    -1.50g = - 45

    g = 30

    This means that there are 30 general admission tickets. Now, you substitute 30 in for g to find s.

    30 + s = 75

    Subtract 30 from both sides.

    s = 45

    This means that there are 30 general admission tickets and 45 student tickets.
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