Adult tickets to a play cost $22. children's tickets cost $15. tickets for a group of 11 people cost $228. write and solve a system of equations to find out how many children and how many adults were in the group

A=22, c=15, and a+c=11, so we can say:
 
a=11-c, then we are told that:

22a+15c=228, using a from above in this equation gives us:

22(11-c)+15c=228 carrying out indicated multiplication

242-22c+15c=228  combining like terms on left side

242-7c=228 subtract 242 from both sides

-7c=-14 divide both sides by -7

c=2, since a=11-c

a=11-2

a=9

So there were 9 adults and 2 children in the group.