In our system of equations, we are going to let the variable c represent the number of children in the group and the variable a represent the number of adults in the group.
We know that there were 11 people in the group, so the number of adults plus the number of children must be 11, or a + c = 11.
We also know the cost of both types of tickets and the total cost, so we can set up a separate equation using each type of ticket’s cost and the respective number of people who purchased it, as follows: 22a + 15c = 228.
Our system of equations is:
a + c = 11
22a + 15c = 228
To solve this system of equations, I am going to use substitution, so we should manipulate the first equation to be one variable in terms of the other. To do this, we should subtract a from both sides, so that we get the following equation:
c = 11 - a
Knowing this, we can substitute in this value for c in the second equation:
22a + 15(11-a) = 228
Now, we must simplify this equation and solve for a:
22a + 165 - 15a = 228
7a = 63
a = 9
This means that 9 adults are in the group. We know that there are 11 total people, so there must be 2 children in the group.
Therefore, your answer is 9 adults and 2 children.
Hope this helps!
