A trader mixes 70%, 64%, and 50% vinegar to make 560 liters of 60% vinegar; how does he mix them if he takes whole liters of each type of vinegar for the mixture?
The merchant buys $x$ liters from the $70 \%$ solution, $y$ from the $64 \%$ solution, and $z$ from the $50 \%$ solution, such that:

$$
x+y+z=560
$$

and

$$
70 x+64 y+50 z=60 \cdot 560
$$

which leads to:

$$
10 x+7 y=2800
$$

Solving this indeterminate equation, we get:

$$
x=7 q, y=400-10 q, z=160+3 q
$$

where $q$ can take any integer value from 0 to 40.

The problem was solved by: Barna D., Brandt D., Devecis M., Kárf J., Lukhaub Gy., Manheim E., Poos M., Rehberger Z., Spitzer Ö., Spitzer S., Szabó I., Weisz J.