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19 August, 11:46

Michael breeds chickens and ducks. last month he sold 50 chickens and 30 ducks for $550 this month he sold 44 chickens and 36 ducks for $532 how much does a chicken cost and how much does aduck cost

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  1. 19 August, 14:05
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    Solution: Let the value of chickens be x and value of ducks be y. 50x + 30y = 550 - - equation 1 44x + 36y = 532 - - equation 2 Balancing the equation, multiplying the equation 1 with 44 and equation 2 with 50. 2200x + 1320y = 24200 - - equation 3 2200x + 1800y = 26600 - - equation 4 Subtract equation 4 from 3, - 480y = - 2400 y = 5 Putting value of y in equation 1, 50x + 30 (5) = 550 50x + 150 = 550 x = 8 Cost of chicken = $8 Cost of duck = $5
  2. 19 August, 14:07
    0
    Let C be the cost of the chicken, and D as the cost of the duck.

    The equation is:

    50c + 30d = 550 (divide this by 10)

    5c + 3d = 55

    3d = 55 - 5c (multiply by 3)

    9d = 165 - 15c

    Afterwards,

    44c + 36d = 532 (divide this by 4)

    11c + 9d = 133

    Substitute the value of 9d:

    11c + 165 - 15c = 133

    11c - 15c = 133 - 165

    -4c = - 32 (divide by - 4)

    c = 8

    Therefore, the cost of each chicken is $8.00

    Now going back to d,

    9d = 165 - 15c (substitute c)

    9d = 165 - 15 (8)

    9d = 165 - 120

    9d = 45 (divide by 9)

    d = 5

    So the cost per duck is $5.00
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