7.1. Kolya and Petya exchanged stamps. Before the exchange, Kolya had 5 more stamps than Petya. After Kolya exchanged $24\%$ of his stamps for $20\%$ of Petya's stamps, Kolya had one stamp less than Petya. How many stamps did the boys have before the exchange?
Answer. Petya had 45 stamps, Kolya had 50 stamps. Solution. Let Petya have $x$ stamps before the exchange, then Kolya had $(x+5)$ stamps. After the exchange, Petya had $x-\frac{x}{5}+(x+5) \cdot \frac{6}{25}$, and Kolya had $x+5-(x+5) \cdot \frac{6}{25}+\frac{x}{5}$. Solving the equation $x-\frac{x}{5}+(x+5) \cdot \frac{6}{25}-x-5+(x+5) \cdot \frac{6}{25}-\frac{x}{5}=1$, we find $x=45$.