Hens and rabbits

There are a certain number of hens and rabbits in a room. The number of feet of the hens exceeds the number of feet of the rabbits by 12, while the number of heads of the hens exceeds the number of the heads of the rabbits by 28. Then the number of hens and rabbits, respectively, in the room are:
A. 60 and 32 B. 50 and 22 C. 52 and 24 D. 48 and 20

Correct answer:

a =  50
b =  22

Step-by-step explanation:

$$\begin{gathered} 2a=4b+12 \\ a=b+28 \\ 2\cdot a=4\cdot b+12 \\ a=b+28 \\ 2a-4b=12 \\ a-b=28 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2a-4b=12 \\ b=22 \\ b=\frac{22}{1}=22 \\ a=\frac{12+4b}{2}=\frac{12+4\cdot 22}{2}=50 \\ a=50 \\ b=22 \\ Bcorrect \end{gathered}$$

Try another example