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This problem involves setting up a system of equations to determine how many tickets were sold to students and non-students.

Let's define two variables:
- Let $ s $ be the number of student tickets sold.
- Let $ n $ be the number of non-student tickets sold.

We know the following information:
1. The total number of tickets sold is 835:
   \[
   s + n = 835
   \]
2. The total revenue from ticket sales is $5792. Student tickets cost $4 and non-student tickets cost $8, so:
   \[
   4s + 8n = 5792
   \]

Now we have the following system of equations:
1. $ s + n = 835 $
2. $ 4s + 8n = 5792 $

We can solve this system to find $ s $ and $ n $.

### Step 1: Solve the first equation for $ s $
\[
s = 835 - n
\]

### Step 2: Substitute this into the second equation
\[
4(835 - n) + 8n = 5792
\]
Simplifying:
\[
3340 - 4n + 8n = 5792
\]
\[
3340 + 4n = 5792
\]
\[
4n = 5792 - 3340
\]
\[
4n = 2452
\]
\[
n = \frac{2452}{4} = 613
\]

### Step 3: Solve for $ s $
Now that we know $ n = 613 $, substitute it back into the equation for $ s $:
\[
s = 835 - 613 = 222
\]

### Conclusion:
- 222 student tickets were sold.
- 613 non-student tickets were sold.

Would you like further details or have any questions about this solution?

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Here are some related questions to further your understanding:
1. How would the solution change if student tickets cost $5 instead of $4?
2. What if the total revenue was $6000 instead of $5792? How would you adjust the system of equations?
3. Can you solve this system of equations graphically?
4. What if the number of non-student tickets sold was known to be 600? How would that change your approach?
5. How can you verify the solution by calculating the total revenue from 222 student tickets and 613 non-student tickets?

**Tip:** When solving word problems, always define your variables and equations clearly, as this helps ensure accuracy when forming the system of equations.

The school athletic council sold 835 tickets to the championship football game for a total of $5792. Students pay $4 and non-students pay $8. How many tickets were sold to students and to non-students?

Learn how to solve a system of equations to determine how many student and non-student tickets were sold at a football game. This problem involves 835 total tickets and a total revenue of $5792, with student tickets priced at $4 and non-student tickets priced at $8. Suitable for students in Grades 7-9.

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