Common denominator of 2 and 5 is 10.

So let there be 10 units of red buttons at first.

Then blue buttons = 10 units + 925

Packed red = ½ = 5/10 of total
That is 5 units out of 10 units
Units left = 10 - 5 = 5


Packed blue = 3/5 of total blue
Blue left = 1 - 3/5 = 2/5 of total blue
= 2/5 of (10 units + 925)

2/5 of 10 units = 4 units
2/5 of 925 = 370

So blue left = 4 units + 370

Total buttons left
= 4 units + 370 + 5 units
= 9 units + 370

And this equals 730.

So 9 units = 730 - 370 = 360
1 unit = 360 ÷ 9 = 40

Total produced
= 10 units + 10 units + 925
= 20 units + 925
= 20 x 40 + 925
= 800 + 925
= 1725

Thank you very much! You are always so helpful, bother to type out and explain. Appreciated.

Most welcome. If you have any doubts do clarify