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Math Help - Cow word problem

  1. #1
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    Unhappy Cow word problem

    A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which gives more milk in a day, a black or brown cow? Show work/explain.


    AND

    CAn you come up with a rectangle whose sides are whole numbers and whose area is numerically equal to its perimeter? There are 2 solutions.
    Area=
    Perimeter=

    THANKS!!!!
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  2. #2
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    Quote Originally Posted by annie3993 View Post
    A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which gives more milk in a day, a black or brown cow? Show work/explain.


    AND

    CAn you come up with a rectangle whose sides are whole numbers and whose area is numerically equal to its perimeter? There are 2 solutions.
    Area=
    Perimeter=

    THANKS!!!!
    Let b = black, r = brown

    (4b + 3r)5 = (3b + 5r)4

    20b + 15r = 12b + 20r

    8b = 5r

    Therefore a brown cow gives more milk in a day.
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  3. #3
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    Quote Originally Posted by annie3993 View Post
    A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which gives more milk in a day, a black or brown cow? Show work/explain.
    Let X be the amount of milk a black cow produces each day.
    Let Y be the amount of milk a brown cow produces each day.

    Therefore, 1 black cow produces 5X of milk in 5 days. So 4 black cows will produce 4x5X=20X in 5 days.
    Similarly, 3 brown cows will produce 3x5Y=15Y of milk in 5 days.

    From the second part (in 4 days), 3 black cows will produce 3x4X=12X of milk in 4 days.
    5 brown cows will produce 5x4Y=20Y of milk in 4 days.


    Therefore, you have the equality : 20X+15Y=12X+20Y

    After some calculations, you should get 8X=5Y

    --> X=\frac 58 Y

    I think you can conclude


    Moo.
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  4. #4
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    Quote Originally Posted by annie3993 View Post
    CAn you come up with a rectangle whose sides are whole numbers and whose area is numerically equal to its perimeter? There are 2 solutions.
    Area=
    Perimeter=

    THANKS!!!!
    h = height, w = width

    hw = 2h + 2w

    w(h - 2) = 2h

    w = 2h/(h-2)

    w is an integer when h-2 is an integer factor of the integer 2h

    We know that 1 will be a factor of 2h, so...

    let h-2 = 1, h = 3, w = 6

    And we know that 2 is a factor of 2h, so...

    let h-2 = 2, h = 4, w = 4
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