Question

At Black Horse Junior School there were altogether 394 teachers and children. The teachers and the boys numbered 189, and the girls and teachers together numbered 217.

1. There were ........ Teachers
2. There were ........ Boys
3. There were ........ Girls

Answer 1

x - teachers
y - boys
z - girls


`x+y+z=394\\ x+y=189\\ x+z=217\\\\ x+y+z=394\\ y=189-x\\ z=217-x\\\\ x+189-x+217-x=394\\ -x=-12\\ x=12\\\\ y=189-12\\ y=177\\\\ z=217-12\\ z=205`