A farmer's heritage

A farmer died leaving his 17 horses to his 3 sons.
When his sons opened up the Will it read:
My eldest son should get 1/2 (half) of total horses;
My middle son should be given 1/3rd (one-third) of the total horses;
My youngest son should be given 1/9th (one-ninth) of the total horses.

How many horses should each son-heir get?

Correct result:

a =  9
b =  6
c =  2

Solution:

q=12+13+19=17180.9444 q1=1q=10.9444=1180.0556 n1=17 a1=n1/2=17/2=172=8.5 b1=n1/3=17/3=1735.6667 c1=n1/9=17/9=1791.8889  n2=1/q1=1/0.0556=18 a=n2/2=18/2=9
b=n2/3=18/3=6b=n_{2}/3=18/3=6
c=n2/9=18/9=2   Verifying Solution:  n3=a+b+c=9+6+2=17



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