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12 May, 21:38

A farmer notes that in a field full of pigs and geese there are 32 heads and 94 feet how many of each animal are there

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  1. 13 May, 00:06
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    There are in total 17 geese and 15 pigs.

    Step-by-step explanation:

    Let us assume the number of geese = m

    Also, the number of pigs = n

    As, there are 32 heads.

    ⇒ m + n = 32 ... (1)

    The number of legs each pig has = 4

    So, the number of legs of n pigs = n (Legs of 1 pig) = n (4) = 4 n

    The number of legs each goose has = 2

    So, the number of legs of m geese = n (Legs of 1 goose) = m (2) = 2 m

    As, there are total 94 feet.

    ⇒ 2 m + 4 n = 94 ... (2)

    Now, solving the given system for the value of m and n:

    m + n = 32 ... (1) ... x[ - 2]

    2 m + 4 n = 94 ... (2)

    Multiply (1) with - 2 and add with (2), w e get:

    -2 m - 2n + 2m + 4n = - 64 + 94

    ⇒ 2n = 30

    ⇒ n = 30/2 = 15

    So, m = 32 - 15 = 17

    Hence there are in total 17 geese and 15 pigs.
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