Final answer:
By setting up a system of equations, we determined that Abigail sold 15 adult tickets and 13 student tickets.
Step-by-step explanation:
Abigail sold adult and student tickets for a total of $226. To solve this problem, we can use a system of equations. Let's assume the number of adult tickets sold is A and the number of student tickets sold is S. We know adult tickets are $9 each and student tickets are $7 each. We also know that Abigail sold a total of 28 tickets.
Here are the two equations we derive from the information provided:
- Equation 1 (for total tickets sold): A + S = 28
- Equation 2 (for total amount collected): 9A + 7S = 226
We can solve this system by substitution or elimination. Let's use substitution:
- From Equation 1, we express A = 28 - S
- We then substitute A in Equation 2: 9(28 - S) + 7S = 226
- Simplify this to 252 - 9S + 7S = 226
- Which further simplifies to -2S = -26
- Dividing by -2, we find S = 13
- Substitute S back into Equation 1: A + 13 = 28
- Finally, we find A = 15
Therefore, Abigail sold 15 adult tickets and 13 student tickets.