16. A function $f(x)$ has the property that, for all positive $x, 3 f(x)+7 f\left(\frac{2016}{x}\right)=2 x$. What is the value of $f(8)$ ?
16. 87 The function $f(x)$ has the property that $3 f(x)+7 f\left(\frac{2016}{x}\right)=2 x$. First observe that $\frac{2016}{8}=252$. Therefore $3 f(8)+7 f(252)=16$ and $3 f(252)+7 f(8)=2 \times 252$. Let $f(8)=V$ and $f(252)=W$. Therefore $3 V+7 W=16$ and $3 W+7 V=504$. When these equations are solved simultaneously, we obtain $V=87$ and $W=-35$ so that $f(8)=87$.