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a florist is making 5 identical bridesmaid bouquets for wedding. she has $510 to spend and wants 20 flowers for each bouquet. roses cost $4 each,tulips cost$2 each and lilies cost $3 each. she wants to have twice as many roses as the other 2 flowers combined in each bouquet. find total number of flowers are there

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  1. For each bouquet:
    Number of lilies --- x
    number of tulips --- y
    number of roses --- 2x + 2y , where both x and y are whole numbers

    then x+y + 2x+2y = 20
    3x + 3y = 20
    x + y = 20/3 <----- trouble ahead: how can the sum of 2 whole numbers be a fraction?

    cost per bouquet = 510/5 = 102
    so 3x + 2y + 4(2x+2y) = 102
    11x + 10y = 102

    first one times 10
    10x + 10y = 200/3
    11x + 10y = 102
    subtract:
    x = 106/3
    y = -86/3 <----- good one!

    2x + 2y = -172/3

    check: 3x + 3y = 3(106/3 + (-86/3) = 20
    total cost: 5(3x + 2y + 4(2x+2y))
    = 55x + 50y
    = 55(106/3) + 50(-86/3) = 510

    So my "solution" to your problem makes mathematical sense,
    but not in the real world.

    I could have stopped at x + y = 20/3
    but I continued to show you the steps you can follow after you fix the problem.

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    Reiny

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