15.1. If
$$
\left\{\begin{array}{l}
w x y=10 \\
w y z=5 \\
w x z=45 \\
x y z=12
\end{array}\right.
$$
what is $w+y$ ?
15.1. $\frac{19}{6}$
We multiply the four given equations.
$$
\begin{array}{c}
(w x y)(w y z)(w x z)(x y z)=10 \cdot 5 \cdot 45 \cdot 12 \\
(w x y z)^{3}=2^{3} 3^{3} 5^{3} \\
w x y z=2 \cdot 3 \cdot 5=30 \\
w=\frac{w x y z}{x y z}=\frac{30}{12}=\frac{5}{2}, \quad y=\frac{w x y z}{w x z}=\frac{30}{45}=\frac{2}{3} \\
w+y=\frac{5}{2}+\frac{2}{3}=\frac{19}{6}
\end{array}
$$