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.
Let's assume the number of adult tickets to be a and the number of children tickets to be c. We can write a system of equations based on the given information.
From the first sentence, we have the equation:
a + c = 11
From the second sentence, we have the equation:
22a + 15c = 228
Using the first equation, we can express c in terms of a:
c = 11 - a
Substituting this value into the second equation, we get:
22a + 15(11 - a) = 228
22a + 165 - 15a = 228
7a + 165 = 228
7a = 63
a = 9
Substituting this value back into the first equation, we get:
9 + c = 11
c = 2
Therefore, there were 9 adults and 2 children in the group.