Question

At the Anderson Little Theater, adult admissions are $4 and

students are $2. If there were 20 more adult tickets sold than
student tickets, and the total receipts for admissions are $314,
how many adults are present?

Answer 1

Using a system of equations, it is determined that there are 59 adults present at the Anderson Little Theater. The number of adult tickets sold is 20 more than student tickets, with adult admissions costing $4 and student admissions $2, totaling $314 in receipts.

Step-by-step explanation:

To solve the question about the number of adults present at the Anderson Little Theater, we need to set up a system of equations based on the given information:

• Adult admissions are $4.
• Student admissions are $2.
• There were 20 more adult tickets sold than student tickets.
• The total receipts for admissions are $314.

Let A be the number of adult tickets sold and S be the number of student tickets sold. Based on the given information we can write the following equations:

1. A = S + 20 (20 more adult tickets than student tickets)
2. 4A + 2S = 314 (Total receipts from ticket sales)

Now we can use substitution to solve the system:

1. Substitute A from the first equation in the second: 4(S + 20) + 2S = 314
2. Simplify and solve for S: 4S + 80 + 2S = 314, which simplifies to 6S + 80 = 314, and then 6S = 314 - 80, which results in 6S = 234
3. Divide both sides by 6 to find S: S = 234 / 6, so S = 39
4. Plug the value of S back into the first equation to find A: A = 39 + 20, therefore A = 59

Therefore, 59 adults are present at the Anderson Little Theater.