3. The arithmetic mean of the numbers $x, y, z, p$ and $q$ is equal to $a$. What is the arithmetic mean of the numbers $x+2y-3, y+2z-1, z+2p, p+2q+1$ and $q+2x+3$?
First method:

Since the arithmetic mean of the numbers $x, y, z, p$ and $q$ is equal to $a$, it follows that $\frac{x+y+z+p+q}{5}=a$ or $x+y+z+p+q=5 a$.

$1 \text{POINT}$

The arithmetic mean of the given numbers is

$$
\begin{aligned}
& \frac{x+2 y-3+y+2 z-1+z+2 p+p+2 q+1+q+2 x+3}{5}= \\
& =\frac{3 x+3 y+3 z+3 p+3 q}{5}= \\
& =\frac{3(x+y+z+p+q)}{5}= \\
& 1 \text{POINT} \\
& =\frac{3 \cdot 5 a}{5}=3 a
\end{aligned}
$$