Part a)
1)
let
x--------> the number of men
y-------> the number of women
z-------> the number of children
we know that
x+y+z=512-----> equation 1
x/y=7/11
x/z=7/14-----> x=z/2-----> equation 2
y/z=11/14----> y=(11/14)z----> equation 3
substitute equation 2 and equation 3 in equation 1
[z/2]+[(11/14)z]+z=512-----> multiply by 14 both sides
7z+11z+14z=7168------> 32z=7168
z=7168/32------> z=224
the answer Part a 1) is
the number of children is 224
Part 2) find the number of men in the film
we know
x=z/2-----> equation 2
z=224
so
x=224/2-----> 112
the answer part a 2) is
112
Part b)
total children=224
total amount=224*($1)*45-----> $10080-----> nearest $100-----> $10100
the answer part b) is
$10100
Part c)
divide 224 by 12
224/12=18.6
so
the smallest possible number of groups is
19
18 groups of 12 children-------> 18*12------> 216
and 1 group of 8 children------> 1*8--------> 8