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27 April, 16:11

1. Suppose a group of 24 people bought tickets to the American Kennel Club Museum of the Dog. Tickets cost $15 each for adults, $10 each for students, and $5 each for children under age 12. There were twice as many adults as children under age 12. If the total cost of the tickets was $260, how many tickets were purchased for children under age 12? * 4 tickets 6 tickets 12 tickets 8 tickets

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  1. 27 April, 16:27
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    Answer: 4 tickets for children under 12.

    Step-by-step explanation:

    A is the number of adults, S is the number of students and C is the number of children.

    We have the equations:

    1) A + S + C = 24.

    2) A = 2*C

    3) A*$15 + S*$10 + C*$5 = $260

    So we have 3 equations and 3 variables.

    First, we can replace A in both of the other equations.

    1) 2*C + S + C = 24

    S + 3*C = 24

    and

    3) (2*C) * $15 + S*$10 + C*$5 = $260

    C * ($30 + $5) + S*$10 = $260

    C*$35 + S*$10 = $260

    Now, we should isolate S in the first equation, and get:

    1) S = 24 - 3*C

    now we can replace it on the other equation:

    3) C*$35 + S*$10 = $260

    C*$35 + (24 - 3*C) * $10 = $260

    C * ($35 - $30) + $240 = $260

    C*$5 = $20

    C = 20/5 = 4

    So we have 4 children.
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