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9 July, 11:34

Ciarra and Ashley sold tickets for the high school basketball tournament. For the opening game of the tournament, girls sold 20 students tickets and 30 non-students tickets and made $190. For the championship game, they sold 50 students tickets and 40 non-students tickets and made $300. What was the price of a student ticket? What was the price of a non-student ticket?

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  1. 9 July, 11:52
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    a = $2, b = $5

    Step-by-step explanation:

    We begin by converting the two scenarios into simultaneos linear equations.

    let a = student tickets and b = non-student tickets

    20a + 30b = $190

    50a + 40b = $300

    from equation 1, 20a + 30b = 190

    a = 190/20 - 30b/20

    a = 9.5 - 1.5b

    Substituting this into equation 2,

    50 (9.5 - 1.5b) + 40b = 300

    475 - 75b + 40b = 300

    475 - 35b = 300

    -35b = 300 - 475

    -35b = - 175

    b = 175/35

    b = $5

    Now we proceed to put the value of b into equation 1;

    20a + 30b = $190

    20a + 30 ($5) = $190

    20a + $150 = $190

    20a = $190 - $150

    20a = 40

    a = $2
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