BALTIC-WAY 2001 Problem 14

There are $2 n$ cards. On each card some real number $x, 1 \leqslant x \leqslant 2$, is written (there can be different numbers on different cards). Prove that the cards can be divided into two heaps with sums $s_{1}$ and $s_{2}$ so that $\frac{n}{n+1} \leqslant \frac{s_{1}}{s_{2}} \leqslant 1$.