16. The real numbers $x$ and $y$ satisfy the equations:
$$
x y-x=180 \text { and } y+x y=208 \text {. }
$$

Let the two solutions be $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$.
What is the value of $x_{1}+10 y_{1}+x_{2}+10 y_{2}$ ?
Solution
317

Subtracting the two equations yields $y+x=28$. Substituting $y=28-x$ into $x y-x=180$ leads to the quadratic equation $0=x^{2}-27 x+180$. This has solutions 12,15 . The solution sets are therefore $(15,13)$ and $(12,16)$.
The value of $x_{1}+10 y_{1}+x_{2}+10 y_{2}$ is $15+10 \times 13+12+10 \times 16=317$.