8.3. In the Banana Republic, parliamentary elections were held in which all residents participated. All those who voted for the "Mandarin" party love mandarins. Among those who voted for other parties, $90\%$ do not like mandarins (the rest do like them). What percentage of the votes did the "Mandarin" party receive in the elections, if exactly $46\%$ of the republic's residents love mandarins?
Answer: $40 \%$.

Solution. Let $x \%$ be the percentage of votes for the party "Mandarin". Then the percentage of votes for the other parties is $(100-x) \%$. One tenth of $(100-x) \%$ love mandarins, so we get the equation $x+(100-x) / 10=46$. Solving this, we find that $x=40$.

## Criteria.

5 points. A correct equation is correctly justified.