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

1.First we have to set up the equations for the problem. The first equation represents the total amount of people in the group. While the second equation represents the cost. In both equations x represents the number of adults while y represents the number of children.
$x+y=11$
$22x+15y=228$
2.Next you must solve the first equation for y.
$y=11-x$
3.Now you must substitute the value of y into the second equation.
$22x+15(11-x)=228$
Next you must multiply every thing in the parentheses by 15.
$22x+165-15x=228$
4.Next you subtract 15x from 22x because they are like terms.
$22x-15x+165=228$
$7x+165=228$
5.Now you must subtract 165 from 228, so that x is on a side by its self.
$7x=228-165$
$7x=63$
6.Now you must divide 63 by 7, so that you find the value of one x not seven.
${\displaystyle x=\frac{63}{7}}$
$x=9$
7.Now place the value you found for x into the original first equation.
$9+y=11$
8.Now subtract 9 from 11 in order to solve for y.
$y=11-9$
$y=2$
Finally check your answers by placing the values you found for x and y into the second equation.
$(22\cdot 9)+(15\cdot 2)=228$
$198+30=228$
$228=228$
There were 9 adults and children.