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.

Question

(1 point)
Responses

2 children, 9 adults
2 children, 9 adults

4 children, 7 adults
4 children, 7 adults

5 children, 6 adults
5 children, 6 adults

7 children, 4 adults

Answer 1

Let's assume that the number of children in the group is represented by c and the number of adults is represented by a.

From the given information, we can create two equations:

1) The total number of people in the group is 11:
c + a = 11

2) The total cost of the tickets for the group is $228:
15c + 22a = 228

We now have a system of equations. To solve it, we can use the substitution or elimination method.

Using the substitution method:

From equation 1), we can express a in terms of c:
a = 11 - c

Substituting this value of a into equation 2):
15c + 22(11 - c) = 228
15c + 242 - 22c = 228
-7c + 242 = 228
-7c = -14
c = 2

Substituting this value of c into equation 1):
2 + a = 11
a = 11 - 2
a = 9

Therefore, there were 2 children and 9 adults in the group.

The correct answer is:
2 children, 9 adults