Question

In a group of cows and chickens, the number of legs was 14 more than twice the number of heads. The number of cows was:

(a) 5, (b) 7, (c) 10, (d) 12, (e) 14​

Answer 1

Answer:

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Step-by-step explanation:

Let the number of cows be x and their legs be 4x.

Let the number of chicken be y and their legs be 2x.

Total number of legs = 4x + 2y.

Total number of heads = x + y.

The number of legs was 14 more than twice the number of heads.

Therefore, 2 × (x + y) + 14 = 4x + 2y.

or, 2x + 2y + 14 = 4x + 2y.

or, 2x + 14 = 4x [subtracting 2y from both sides].

or, 14 = 4x – 2x [subtracting 2x from both sides].

or, 14 = 2x.

or, x = 7 [dividing by 2 on both sides].

Therefore, the number of cows = 7.

Answer: (b)

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Answer 2

Let no. of cosws

=

x

& no. of chickens

=

y

∴ total no. of heads

=

x+

y

& Total no. of legs

=

4×

xf2×

y

= 4x+ 2y

Now, given that no. of legs is 14 more than twice no of heads.

∴ 2(x+ y)+ 14= 4x+ 2y

∴ 2x+ 2y+ 14= 4x+ 2y

−(1)

∴ 14= 2x

∴ x= 7⇒ No. of cows.