2/3 of the blue beads were used. So 1/3 of blue beads are left.


ratio of red to blue beads at the end = 2 : 5

So 1/3 of blue beads = 5 units
Total blue beads = 5 units x 3 = 15 units

Notice that the ratio at the start is 3 : 5.

But the total number of blue beads is 15 units. So we change the ratio.

3 : 5 = 9 : 15

so we have 9 units of red beads and 15 units of blue beads at first.

Red beads used
= 9 units - 2 units
= 7 units

7 units = 21 beads
1 unit = ?

From here you should be able to solve.