Chickens and Cows

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When asked how many chickens and cows he had on his farm Mr Brown refused to answer directly, but he did say that the total number of heads was 30 and the total number of legs was 100. How many of each was there?

Comments

  1. Anonymous4 February 2021 at 12:42

    We can start off by creating some equations.

    We can call the chickens "x" and the cows "y"
    If there were 30 heads in total and both chickens and cows have 1 head then our equation would be:

    x + y = 30

    For the next equation, chickens have 2 legs and cows have 4 meaning our equation will be:

    2x + 4y = 100

    We can multiply the first equation by -2 to get -2x - 2y = -60.
    If we add that to the first equation we get 2y = 40 so y = 20.

    Now that we know the total number of cows are 20, to find the total number of chickens we need to substitute cows into the first equation.

    x + 20 = 30

    This would mean that x = 10

    Now we have our answer:
    Total number of cows: 20
    Total number of chickens: 10

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