Question

It's about equation systems with two incognitos. "In a farm exists chickens and lambs. There are 31 animals in total and 82 legs. how many chickens and lambs are there?

Answer 1

Answer:

$there \: are \: \boxed{10 \: chickens }\: and \: \boxed{21 \: lambs}$

Step-by-step explanation:

$chickens \: and \: lambs \: = 31. \\ but \: chickens \: have \: 2 \: legs \\ while \\ lambs \: have \: 4 \: legs \\ let \: chickens\: be \to \: c \\ let \: lambs\: be \to \: l \: \\ so : 2l + 4c = 82 \\ but \: c + l = 31 \\ l = 31 - c \\ hence \to \\ 2(31 - c) + 4c = 82 \\ 62 - 2c + 4c = 82 \\ 2c = 82 - 62 \\ 2c = 20 \\ \boxed{c = 10} \\ l = 31 - c \\ l = 31 - 10 \\ \boxed{l = 21}$

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