2. For the visit to the Ivan Meštrović exhibition, $\frac{2}{7}$ more students registered than planned. Due to illness, one-sixth of the registered students canceled, and as a result, six more students went to the exhibition than planned. How many students went to the exhibition?
First solution.

Let $x$ be the planned number of students who were supposed to visit the exhibition.

The number of students who registered for the exhibition visit is $x+\frac{2}{7} x=\frac{9}{7} x$, i.e., $\frac{9}{7}$ of the planned number.

Due to illness, $\frac{1}{6} \cdot \frac{9}{7} x=\frac{3}{14} x$ students dropped out, i.e., $\frac{3}{14}$ of the planned number.

The number of students who went to the exhibition is $\frac{9}{7} x-\frac{3}{14} x=\frac{15}{14} x$, i.e., $\frac{15}{14}$ of the planned number.

1 POINT

Thus, $\frac{15}{14} x - x = \frac{1}{14} x$ students went to the exhibition, i.e., $\frac{1}{14}$ more than planned.

We have $\frac{1}{14} x = 6$,

so $x = 6 \cdot 14 = 84$.

It was planned that 84 students would go to the exhibition, and 6 more students went, so the total number of students who went to the exhibition is 90.

1 POINT

TOTAL 6 POINTS

Note: If a student sets up the equation $x + 6 = \frac{5}{6} \cdot \frac{9}{7} x$ which leads to the planned number of students, they earn 3 POINTS. Solving this equation correctly earns an additional 2 POINTS. The final solution of 90 earns 1 POINT.