Problem 3. Determine the numbers $a, b$, and $c$, if their sum is $\frac{5}{2}$ greater than the number $a$, $\frac{59}{6}$ greater than the number $b$, and $\frac{5}{3}$ greater than the number $c$.
Solution. From the condition of the problem, the following equalities are written:

$$
a+b+c=a+\frac{5}{2}, a+b+c=b+\frac{59}{6} \text { and } a+b+c=c+\frac{5}{3} \text {. }
$$

By rearranging the equations, we get $b+c=\frac{5}{2}, a+c=\frac{59}{6}$ and $a+b=\frac{5}{3}$. By adding the three equations, we get $2 a+2 b+2 c=14$, i.e.

$$
a+b+c=7
$$

By substituting (2) into the equations from (1), we get

$$
7=a+\frac{5}{2}, 7=b+\frac{59}{6}, 7=c+\frac{5}{3}
$$

from which it follows that $a=\frac{9}{2}, b=-\frac{17}{6}, c=\frac{16}{3}$.