68. Find two numbers, the ratio of which is 3, and the ratio of the sum of their squares to their sum is 5.
68. $\frac{x}{y}=3 ; \frac{x^{2}+y^{2}}{x+y}=5$.

By squaring both sides of the first equation term by term, we get:

$$
\frac{x^{2}}{y^{2}}=9 \text { and } \frac{x^{2}+y^{2}}{y^{2}}=10
$$

Comparing with the second equation gives:

$$
\begin{aligned}
10 y^{2} & =5(x+y) \\
2 y^{2} & =x+y
\end{aligned}
$$

but $x=3 y$, therefore, $2 y^{2}=4 y ; y=2 ; x=6$.