2. Maša had three necklaces with different numbers of beads. From them, she made three new necklaces, each with 80 beads. She did this by removing $\frac{3}{7}$ of the beads from the first necklace and moving them to the second necklace, then from the resulting second necklace, she moved $\frac{3}{7}$ of the beads to the third necklace, and finally from the resulting third necklace, she moved $\frac{3}{7}$ of the beads back to the first. How many beads were on each of the three necklaces before the transfer?
First solution.

After the last transfer of $\frac{3}{7}$ of the beads from the third to the first necklace, there were 80 beads left on the third necklace.

Before the transfer, there were $\frac{7}{4} \cdot 80=140$ beads on the third necklace. 2 POINTS

This means that $\frac{3}{7} \cdot 140=60$ beads were transferred to the first necklace, $\quad 1$ POINT

so there were $80-60=20$ beads on the first necklace.

$1 \text{ POINT}$

We similarly conclude for the other transfers.

|  | 1st necklace | 2nd necklace | 3rd necklace |
| :--- | :---: | :---: | :---: |
| At the end | 80 | 80 | 80 |
| Before 3rd transfer | 20 | 80 | 140 |
| Before 2nd transfer | 20 | 140 | 80 |
| Before 1st transfer | 35 | 125 | 80 |

TOTAL 10 POINTS