Two brigades together produced 8200 transformer windings. The inspection found $2 \%$ of the windings from one brigade and $3 \%$ of the windings from the other brigade to be improperly insulated, totaling 216 units. How many faultless windings did each brigade produce?
I. Solution. If the second brigade had also worked with only a 2% defect rate, then $8200 \cdot 0.02 = 164$ units would have been defective, 52 fewer than the actual data. This difference represents 1% of the second brigade's production, so they must have produced 5200 units for inspection, and the first brigade produced 3000 units. The number of non-defective units from the first brigade is $3000 \cdot 0.98 = 2940$, and from the second brigade, $5200 \cdot 0.97 = 5044$.

Földes Antónia (Budapest, Apáczai Csere J. Practical Grammar School II. Class)

II. Solution. Denoting the number of rolls produced by the first brigade as $x$, the second brigade's production is $8200 - x$ units, and the number of defective rolls is $0.02x$ and $0.03(8200 - x)$, respectively. Their sum is:

$$
0.02x + 0.03(8200 - x) = 216
$$

from which $x = 3000$, and $8200 - x = 5200$. Thus, the number of non-defective rolls is 2940 and 5044, respectively.

Szilágyi Gábor (Ózd, Bartók B. Secondary School VIII. Class)

Note. The first solution shows that equations are not necessary to solve the problem. In school, solving easy problems with equations is often done to familiarize students with the method. Nevertheless, we recommend that solvers keep in mind that equations are not necessary for solving such easy problems.