Question

A farmer has some hens and some goats. If the total number of animal heads is $80$ and the total number of animal feet is $200$, what is the total number of goats?

• A. $40$
• B. $60$
• C. $20$
• D. Cannot be determined

Answer 1

Answer: (C)

Let the number of goats $=x$

the number of hens $=y$

It is given that, Total umber of animals $=80$

$\Rightarrow x+y=80$ ---(1)

As per fact that, each hen has $2$ legs and each goat has $4$ legs and it is given that, total umber of legs are $200$.

$\Rightarrow 4x+2y=200$ ---(2)

From (1),

$\Rightarrow x+y=80$

$\Rightarrow x=80-y$

Lets substitute $x=80-y$ in $4x+2y=200$

$\Rightarrow 4(80-y)+2y=200$

$\Rightarrow 320-4y+2y=200$

$\Rightarrow 320-2y=200$

$\Rightarrow -2y=200-320$

$\Rightarrow -2y=-120$

$\Rightarrow 2y=120$

$\Rightarrow y=\frac{120}{2}$

$\Rightarrow y=60$

$\Rightarrow$ number of hens are $60$.

Now, lets substitute $y=60$ in $x+y=80$

$\Rightarrow x+60=80$

$\Rightarrow x=80-60=20$

$\Rightarrow$ the number of goats $=20$

Hence, Option $B$ is correct.