Afarmhouse shelters 18 animals. some are cows and some are chickens. altogether there are 68 legs how many of each animal are there?

The number of cows in farmhouse shelter is 16

The number of chickens in farmhouse shelter is 2   .

Step-by-step explanation:

Total number of animals in farmhouse shelters = 18

Total number of legs of both animals = 68 legs

Let The number of cows = C

Let The number of chickens = c

∵  the number of legs does each cow has = 4

And, The number of legs does each chicken has = 2

According to question

∵Total number of animals in farmhouse shelters = 18

i.e number of cows + number of chickens = 18

Or, C + c = 18                       .....1

Again

∵ Total number of legs of both animals = 68 legs

i.e  number of cows × number of legs does each cow has + number of chickens × number of legs does each chicken has = 68

Or, C × 4 + c × 2 = 68

i.e 4 C + 2 c = 68                     ........2

Solving eq 1 and eq 2 , we get

(4 C + 2 c ) - 2 × (C + c) = 68 - 2 × 18

Or, (4 C - 2 C) + (2 c - 2 c) = 68 - 36

Or, 2 C + 0 = 32

∴  C =

i.e C = 16

So, The number of cows in farmhouse shelter = C = 16

Again

Put the value of C into eq 1

∵ C + c = 18

Or, c = 18 - C

Or, c = 18 - 16

i.e c = 2

So, The number of chickens in farmhouse shelter = c = 2

Hence, The number of cows in farmhouse shelter is 16 and The number of chickens in farmhouse shelter is 2   . Answer

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