13.049. The first of the unknown numbers is $140\%$ of the second, and the ratio of the first to the third is 14/11. Find these numbers if the difference between the third and the second is 40 units less than the number that is $12.5\%$ of the sum of the first and second numbers.
Solution.

Let $x$ be the first number. Then $\frac{1}{1.4} x$ is the second number, and $\frac{11}{14} x$ is the third number. According to the condition, $\frac{11}{14} x - \frac{1}{1.4} x + 40 = 0.125 \left(x + \frac{1}{1.4} x\right)$, from which $x = 280$. The second number is $-\frac{280}{1.4} = 200$; the third is $-\frac{11}{14} \cdot 280 = 220$.

Answer: 280, 200, 220.