Problem 8.2. In the chat of students from one of the schools, a vote was held: "On which day to hold the disco: October 22 or October 29?"

The graph shows how the votes were distributed an hour after the start of the voting.

Then, 80 more people participated in the voting, voting only for October 22. After that, the voting ended. The final distribution of votes is also shown on the graph.

How many people participated in the voting?

![](https://cdn.mathpix.com/cropped/2024_05_06_df4c0436ab68970fab15g-24.jpg?height=494&width=747&top_left_y=1295&top_left_x=339)
Answer: 260.

Solution. Let $x$ be the number of people who voted an hour after the start. From the left chart, it is clear that $0.35 x$ people voted for October 22, and $-0.65 x$ people voted for October 29.

In total, $x+80$ people voted, of which $45\%$ voted for October 29. Since there are still $0.65 x$ of them, we get the equation

$0.65 x=0.45(x+80)$, from which we find $x=180$. Therefore, a total of $180+80=260$ people participated in the voting.