Algebra

On the opening night of a play at a local theatre, 895 tickets were sold for a total of $10,514. Adult tickets cost $14 each, children's tickets cost $11 each and senior citizen tickets cost $8 each. If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 295, than how many tickets of each type were sold?

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  1. adults --- x
    children -- y
    seniors --- z

    x+y+z = 895 , #1

    14x +11y + 8z = 10514 , #2

    translation of:
    "If the combined number of children and adult tickets exceeded twice the number of senior citizen tickets by 295"
    ---> x+y > 2z by 295
    x+y = 2z + 295
    x + y - 2z = 295 #3

    #1 - #3:
    3z = 600
    z = 200
    so #1
    ---> x+y + 200 = 895
    y= 695 - x

    sub into #2:
    14x + 11(695-x) +8(200) = 10514
    14x + 7645 - 11x + 1600 = 10514
    3x = 1269
    x = 423
    then y = 695 - 423 = 272

    So they sold
    423 adult
    272 children and
    200 senior tickets

    checK
    14(423) + 11(272) + 8(200) = 10514, YEAHHH

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  2. Ticket Sales. Stacey is selling tickets to the school play. The tickets are $7 for adults and $4 for children. She sells twice as many adult tickets as children's tickets and brings in a total of $306. How many of each kind of ticket did she sell?

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