let's set 'a' as the coins the first brother recieves (the youngest) and for every older brother, we will add 'x' (the constant number)
Since we know the sum has to be equal to 100, our equation is:
100=a+(a+x)+(a+2x)+(a+3x)+...+(a+8x)+(a+9x)
the 7th oldest brother is the 3rd youngest, therefore, if we look at our equation, he gets (a+2x) - we know now that 7=a+2x
We can now simplify the first equation by summing up our 'x' and 'a'
we get: 100=10a+45x
In order to resolve the equation (since we have 2 variables), we can use the subtraction method
100=10a+45x
-10(7=a+2x)
100=10a+45x
-(70=10a+20x)
30=25x
1.2 = x
and for 'a' -> 7 = a +2(1.2)
a=4.6
Therefore, the youngest gets 4.6 coins (a), the second 5.8 (a+x) ...
