How Many Child, Ladies And Gents Are There In The Family?

One family of 20 members have 20 chapatis to eat, finally

Every child gets 1/2 chapati.
Every Lady in the house gets 2 chapatis.
And every gentleman gets 3 chapatis to eat.

How many Child, Ladies and Gents are there in the family?

Answer with Logic :
Lets assume number of children are X
number of ladies are Y
number of gents are Z

Now 
X+Y+Z = 20 ;
1/2 x + 2 Y + 3 Z = 20 ;
and X,Y,Z are integers and greater then or equal to zero.

Now we can deduce -
X is even
y < 10 and Z < 6

Now try trial and error after removing one variable from able two equations (i.e. 3y+5z = 20) which gives as y=0 & z=4 and y=5 & z=1. Second solution fits in the above equations so,

number of children X = 14
number of ladies Y = 5
number of gents Z = 1