13.034. In a store, textbooks on physics and mathematics were received for sale. When $50\%$ of the mathematics textbooks and $20\%$ of the physics textbooks were sold, which amounted to a total of 390 books, the remaining mathematics textbooks were three times as many as the remaining physics textbooks. How many textbooks on mathematics and how many on physics were received for sale?
Solution.

Let $x$ be the number of mathematics textbooks and $y$ be the number of physics textbooks available for sale. The number of textbooks sold is $0.5 x + 0.2 y = 390$. The remaining textbooks are $0.5 x$ mathematics textbooks and $0.8 y$ physics textbooks. According to the condition, $\frac{0.5 x}{0.8 y} = 3$. Solving the system $\left\{\begin{array}{l}0.5 x + 0.2 y = 390 \\ \frac{0.5 x}{0.8 y} = 3\end{array}\right.$, we get $x = 720$; $y = 150$.

Answer: 720 and 150.