[ Inequality problems. Case analysis]

Lёsha and Ira live in a house where each floor has 9 apartments (the house has one entrance). The floor number of Lёsha is equal to the apartment number of Ira, and the sum of their apartment numbers is 329. What is the apartment number of Lёsha?
Let $K$ be the apartment number of Ira (and the floor number of Lёsha). Then the apartment number of Lёsha is between $9K-8$ and $9K$, which means the sum of the apartment numbers of the kids is from $10K-8$ to $10K$. The system of inequalities $10K-8 \leq 329 \leq 10K$ has a unique solution: $K=33$. And Lёsha lives in apartment number $329-33=296$.

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