3. (10 points) In a cage, there are chickens and rabbits, with a total of 51 heads. The total number of rabbit feet is 4 more than 3 times the total number of chicken feet. Therefore, there are $\qquad$ rabbits in the cage.
【Analysis】According to the problem, if one rabbit is less, then the total number of rabbit feet is three times the total number of chicken feet. Since the number of feet of one rabbit is $4 \div 2=2$ times the number of feet of one chicken, the total number of rabbit feet is three times the total number of chicken feet when the number of rabbits is $3 \div 2=1.5$ times the number of chickens. Therefore, the number of chickens is $(51-1) \div(1.5+1)=20$. From this, we can find the number of rabbits.

【Solution】Solution: $4 \div 2=2$
$$
\begin{aligned}
& (51-1) \div(3 \div 2+1) \\
= & 50 \div 2.5 \\
= & 20 \text { (heads) }
\end{aligned}
$$
$51-20=31$ (heads)
Answer: There are 31 rabbits in the cage.
Therefore, the answer is: 31.