G7.3-G7.4 Chicken eggs cost $\$ 0.50$ each, duck eggs cost $\$ 0.60$ each and goose eggs cost $\$ 0.90$ each. A man sold $x$ chicken eggs, $y$ duck eggs, $z$ goose eggs and received $\$ 60$. If $x, y, z$ are all positive numbers with $x+y+z=100$ and two of the values $x, y, z$ are equal,

G7.3 find $x$.
G7.4 find $y$.
$$
\begin{array}{l}
0.5 x+0.6 y+0.9 z=60 \\
\Rightarrow 5 x+6 y+9 z=600 \ldots \ldots \\
x+y+z=100 \ldots \ldots(2)
\end{array}
$$

If $x=z$, then $14 x+6 y=600$
$\Rightarrow 7 x+3 y=300$ $\qquad$ (3) and $2 x+y=100$ $\qquad$
(3) $-3(4): x=0$ (rejected)

If $x=y$, then $11 x+9 z=600$ $\qquad$ (5) and $2 x+z=100$ $\qquad$ $9(6)-(5): 7 x=300, x$ is not an integer, rejected.
(1) $-5(2): y+4 z=100$ $\qquad$
If $y=z$, then $y=z=20, x=60$