28.1. A pile contains 100 weights, each weighing either 1 g, 10 g, or 50 g. How many weights of each kind are in the pile if they all together weigh 500 g.

$$
(7-9 \text { grade })
$$
28.1. Let the number of weights of each of the specified values be denoted by $a, b, c$ respectively. Based on the problem statement, we have the system of equations:

$$
\left\{\begin{array}{l}
a+b+c=100 \\
a+10 b+50 c=500
\end{array}\right.
$$

Subtracting the first equation from the second, we get:

$$
9 b+49 c=400, \text { from which } b=(400-49 c): 9 .
$$

Considering that $b$ is a non-negative integer, we conclude that the values of $c$ to be tested range from 0 to 8. Checking shows that only when $c=1$ does the expression $400-49 c$ divide by 9. In this case, $b=39$. Now, from the first equation of the system, we find that $a=60$. Answer: $a=60, b=39, c=1$.