Question

Abigail's school is selling adult tickets and student tickets for a play. Adult tickets are $9 each, and student tickets are $7 each. She sold a total of 28 tickets and collected $226. How many adult tickets did she sell? How many student tickets did she sell?

a) Adult tickets sold: 12, Student tickets sold: 16
b) Adult tickets sold: 16, Student tickets sold: 12
c) Adult tickets sold: 10, Student tickets sold: 18
d) Adult tickets sold: 18, Student tickets sold: 10

Answer 1

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.