In 1966, there were 30 more women than men living in the village of Bezdíkov. To the present day, the number of women living in the village has decreased fourfold, and the number of men living in the village has decreased by 196. Now, there are 10 more women than men in Bezdíkov.

How many women and men in total live in Bezdíkov today?

(L. Simünek)
The difference between the original number of women and the current number of men is $30+196=226$, which is 10 more than the difference between the original and current number of women. This means that three quarters of the original number of women are equal to $226-10=216$. The remaining one quarter, corresponding to the current number of women, is thus $216: 3=72$. The number of men is now $72-10=62$.

In the village, there are now a total of $62+72=134$ men and women.

The previous considerations can be graphically illustrated as follows:

![](https://cdn.mathpix.com/cropped/2024_04_17_eaf15ad62c30ffd7ab50g-1.jpg?height=540&width=1442&top_left_y=1038&top_left_x=313)

Note. The current number of women can be determined algebraically by solving the equation. If we denote this number by $z$, then the original number of women was $4z$, the current number of men is $z-10$, and the original number of men was $4z-30$. The difference between the original and current number of men is 196, so:

$$
\begin{aligned}
(4 z-30)-(z-10) & =196 \\
3 z-20 & =196 \\
z & =72 .
\end{aligned}
$$

Scoring suggestion. 2 points for the current number of women; 1 point for the correct conclusion; 3 points based on the quality of the explanation.