13.017. Find the sum of three numbers, knowing that the third is related to the first as $18.48: 15.4$ and constitutes $40 \%$ of the second, and the sum of the first and second is 400.
Solution.

Let $x, y, z$ be the given numbers. According to the condition, we have: $\frac{z}{x}=\frac{1848}{1540}=\frac{6}{5}$, $z=0.4 y, x+y=400$. Since $y=\frac{5}{2} z$ and $z=\frac{6}{5} x$, then $y=3 x$ and $x+3 x=400 \Rightarrow$ $\Rightarrow x=100, z=\frac{6}{5} x=120$. Then

$S=x+y+z=400+120=520$.

Answer: 520.