## 36. Daily Newspapers

In a small town where many vacationers spend their holidays, $28 \%$ of the adult vacationers read "Mond", $25 \%$ read "Figaro", and $20 \%$ read "Orore". Additionally, $11 \%$ of the vacationers read both "Mond" and "Figaro", $3 \%$ read both "Mond" and "Orore", and $2 \%$ read both "Figaro" and "Orore", while $42 \%$ of the vacationers do not read any of these three newspapers. What is the percentage of adult vacationers who read all three newspapers, "Mond", "Figaro", and "Orore"?
36. Let $x$ be the desired percentage. Denote by $V$ the set of all vacationers, by $M$ the set of "Mond" readers, by $F$ the set of "Figaro" readers, and finally by $A$ the set of "Aurore" readers. To determine the desired percentage, we will use the Venn diagram provided below.

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-120.jpg?height=434&width=768&top_left_y=865&top_left_x=650)

The entire set $V$ corresponds, of course, to $100 \%$. From this, we obtain the equation

$$
\begin{gathered}
42+(14+x)+(12+x)+(15+x)+(11-x)+ \\
+(2-x)+(3-x)+x=100
\end{gathered}
$$

i.e., $x=1 \%$.

Thus, $1 \%$ of adult vacationers read all three newspapers simultaneously.