Question

The admission fee for a school play is $3.00 for studnets (s) and $5.00 for non- students (n). On opening night 200 people attened and $800 is collected. How many students and how many non-students attended?

Answer 1

To solve the problem, we can set up a system of equations based on the information given.

Let:
- \( s \) = number of students
- \( n \) = number of non-students

From the information given, we can form the following equations:

1. The total number of attendees is 200:
\[
s + n = 200
\]

2. The total revenue collected from tickets is $800:
\[
3s + 5n = 800
\]

Now, we can solve this system of equations.

First, we can solve Equation 1 for \( n \):
\[
n = 200 - s
\]

Next, substitute this expression for \( n \) into Equation 2:
\[
3s + 5(200 - s) = 800
\]

Distributing the 5:
\[
3s + 1000 - 5s = 800
\]

Combine like terms:
\[
-2s + 1000 = 800
\]

Subtract 1000 from both sides:
\[
-2s = 800 - 1000
\]
\[
-2s = -200
\]

Dividing both sides by -2:
\[
s = 100
\]

Now we can find \( n \) using the value of \( s \):
\[
n = 200 - s = 200 - 100 = 100
\]

So, the solution is:
- Number of students \( s = 100 \)
- Number of non-students \( n = 100 \)

In conclusion, there were 100 students and 100 non-students who attended the play.