## Task 1 - 330821

At the beginning of a party, there were in total: Exactly four times as many women as men. After four couples left the party, there were exactly five times as many women as men at the party.

How many people were there in total at the beginning of the party?
If at the beginning there were exactly $x$ men at the party, then there were exactly $4 x$ women at the party. After four couples left the party, exactly $x-4$ men and $4 x-4$ women remained. For these numbers, it follows that

$$
5 \cdot(x-4)=4 x-4 \quad \text { so } \quad x=16
$$

Thus, at the beginning there were 16 men and 64 women, making a total of 80 people at the party.