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19 November, 10:01

A theater charges $25 for adults and $15 for children. When the price of a child's ticket increases to $18 next year, the cost for a dance club to attend the theater will increase from $450 to $480. Write and solve a system of equations to find how many adults are in the dance club.

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  1. 19 November, 10:30
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    Given:

    tickets for adults - 25

    tickets for kids - 15

    initial cost - 450

    increase in tickets for kids to - 18

    cost after increase - 480

    let x be number of adults and y be number of kids

    25x + 15y = 450

    25x + 18y = 480

    subtraction:

    25x + 15y = 450

    -25x - 18y = - 480

    0 - 3y = - 30

    y = - 30/-3

    y = 10

    There are 10 kids.

    25x + 15y = 450

    25x + 15 (10) = 450

    25x + 150 = 450

    25x = 450 - 150

    25x = 300

    x = 300/25

    x = 12

    There are 12 adults.

    All in all there are 12 adults and 10 kids.

    to check:

    25x + 15y = 450

    25 (12) + 15 (10) = 450

    300 + 150 = 450

    450 = 450

    25x + 18y = 480

    25 (12) + 18 (10) = 480

    300 + 180 = 480

    480 = 480
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