algebra(help)

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2000 tickets were sold for a play generating 19,700. The prices of the tickets were $5 for children, $10 for students and $12 for adults. There were 100 more adult tickets sold than students. Find the number of each type ticket sold.

Find the number of each type sold.

Thanks for your help.

  • algebra(help) -

    student tickets ---- x
    adult tickets ------- x+100
    children tickets ---- 2000 -x - (x+100) = 1900-2x

    5(1900-2x) + 10x + 12(x+100) = 19700
    9500 - 10x + 10x + 12x + 1200 = 19700
    12x = 9000
    x = 750 student tickets
    x+100 = 850 adult tickets
    leaving 400 children tickets


    check:
    5(400) + 10(750) + 12(850) = 19700

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