## Task B-1.5.

Three friends Marta, Iva, and Ana love to travel. Marta has visited 20 countries, Iva has visited $90\%$ more countries than Marta, and Ana has visited 13 fewer countries than Iva. Ana has visited $40\%$ of the countries Marta has visited, and Iva has visited one-fifth of the countries Ana has visited and half of the countries Marta has visited. The number of countries visited by all three friends is 16 times smaller than the total number of countries they have visited. How many countries have they visited in total?
## First solution.

Let $k(M)$ be the number of countries visited by Marta, $k(I)$ the number of countries visited by Iva, and $k(A)$ the number of countries visited by Ana. Then, according to the conditions of the problem,

$$
\begin{array}{cc}
k(M)=20, k(I)=38, k(A)=25 . & 1 \text { point } \\
k(M \cap A)=8, k(I \cap A)=5, k(M \cap I)=10 . & 1 \text { point }
\end{array}
$$

Let $x$ be the number of countries visited by all friends, i.e., $k(M \cap I \cap A)=x$.

Then $k(M \cup I \cup A)=16 x$, and by applying the formula

$k(M \cup I \cup A)=k(M)+k(I)+k(A)-k(M \cap A)-k(I \cap A)-k(M \cap I)+k(M \cap I \cap A) \quad 1$ point

we get

$$
16 x=20+38+25-8-5-10+x
$$

which simplifies to $x=4$.

The friends have visited a total of 64 countries.