Suppose that there are $1650$, $1560$ and $1260$ lamps of three types A, B, C respectively. I want to distribute them in boxes with equal sizes so that each box contains the maximum number of lamps of a certain type.
My attempt:
The formula I can think of is:
$$1650+x_1 = 1560+x_2=1260+x_3$$ $$x_1+x_2+x_3 =0$$
However, I still need another equation to solve this problem. In general, what is the easy way to solve such problems?
We have $$\gcd(1560,1650,1260)=30$$therefore you can put the lamps in boxes with capacity of 30 each containing only one certain type and there are 149 such boxes there