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
