ANSWER.  70 kids, 19 men and 11 women.


CHECK.   counting people  70 + 19 + 11 = 100.

         counting cents  7 (kids) + 38 (men) + 55 (women) = 100 cents.



Solution.


You have 2 equations


    k  +  m +  w = 100     (1)      (counting people)

     + 2m + 5w = 100    (2)      (counting cents)


Multiply equation (1) by 2 (both sides).  Keep equation 2 as is.  You get


    2k +  2m + 2w = 200    (3)      

     + 2m + 5w = 100    (4)     


From equation (3), subtract equation (4).  You get


    1.9k            + 3w = 100.


So,  w = .


From this equation, find w in a way to get the INTEGER NUMBER.


REMEMBER that  "k"  is  (should be)  multiple of  10.


Then you will find  k = 70, w = 11  .