42. There are 3 grams, 7 grams, and 14 grams weights totaling 11, with a total weight of 108 grams. How many of each weight are there? $\qquad$个, $\qquad$个, $\qquad$个.
Answer: $1,5,5$
Solution: Let the number of 3g, 7g, and 14g weights be $x, y, z$ respectively,

From the problem, we have
$$
\left\{\begin{array}{l}
x+y+z=11 \\
3 x+7 y+14 z=108
\end{array},\right.
$$

Eliminating $x$, we get
$$
4 y+11 z=75 \text {, }
$$

Thus,
$$
z=7-\frac{2+4 y}{11},
$$

Combining that $y$ and $z$ are positive integers, we get
$$
\left\{\begin{array}{l}
y=16 \\
z=1
\end{array},\left\{\begin{array}{l}
y=5 \\
z=5
\end{array},\right.\right.
$$

The corresponding solutions are
$$
x=-6 \text { (discard), } x=1 \text { . }
$$

Therefore, the number of 3g, 7g, and 14g weights are $1,5,5$ respectively.