c - number of children
a - number of adults
c+a=152
13a - was paid for adult's tickets
5c - was paid for child's tickets
13a+5c = 1096
13a+5c = 1096
(a+c=152) * -13 ----> -13a - 13c = -15213 ---->-13a - 13c = -15213=-1976
13a+5c = 1096
-13a - 13c=-1976
8c =-880
c=110
c+a=152
110+a=152
a=42
Check:
1342+5110 = 1096
1096=1096 True