math

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I have 50.00 to buy 50 animals. Chickens are .50, cows are 2.50,and birds are 5.00. How many of each animal can i purchase?

  • math -

    Divide each of those numbers by 50

  • math -

    Then you must balance it all out
    So 50/.5=100
    50/2.5=20
    50/5=10

  • math -

    number of chickens --- x
    number of cows ------- y
    number of birds -------50-x-y

    .5x + 2.5y + 5(50-x-y) = 50
    times 10
    5x + 25y + 50(50-x-y) = 500
    5x + 25y + 2500 - 50x - 50y = 500
    -45x -25y = -2000
    9x + 5y = 400
    we need integer solutions , where both x and y must be between 0 and 50
    clearly (0,80) would be a solution to our equation, but not permitted since we only have a total of 50 animals.
    BUT, I also know that the slope of the line is -9/5
    so if we decrease the y by 9 and increase the x by 5 we get more integer solutions to our equation:

    0 80
    5 71
    10 62
    15 53
    20 44
    25 35
    30 26
    35 17
    40 8

    45 -1

    but remember that 50-x-x also has to be a positive whole number
    the only combination that works is
    x =40, y = 8
    then 50-x-y = 2

    so we have 40 chickens
    8 cows
    2 birds


    check:
    40+8+2 = 50
    .5(40) + 2.5(8) +5(2) = 50
    Yeahhh!!!

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