The fraction

$$
\frac{306 x^{2}-450 x+162}{(8 x-7)(5 x-4)(2 x-1)}
$$

is to be decomposed into the sum of 3 fractions, whose denominators are: $(8 x-7), \quad(5 x-4), \quad(2 x-1)$.
Let the numerators of the fractions be: $a, b$ and $c$. Eliminate the denominators, arrange the entire expression in descending powers of $x$, and bring all terms to one side. Since the resulting expression is equal to 0 for all values of $x$, it follows that the coefficients of $x^2$, $x$, and the constant term must all be equal to 0. This gives us the following equations:

$$
\begin{gathered}
10 a+16 b+40 c-306=0 \\
13 a+22 b+67 c-450=0 \\
4 a+7 b+28 c-162=0
\end{gathered}
$$

Solving this system of equations, we get: $a=9, b=6, c=3$.

(Zoltán Pénzes, 6th grade, Arad.)

The problem was also solved by: Déri Zs., Deutsch I., Haar A., Jánosy Gy., Kelemen M., Kertész G., Kürti I., Messer P., Neidenbach E., Söpkéz Gy.