Tickets of a program at college cost ​$4 for general admission or ​$3 with a student ID. If 181 people paid to see a performance and ​$618 was​ collected, how many of each type of ticket were​ sold?

Let:
- $ x $ be the number of general admission tickets sold.
- $ y $ be the number of student tickets sold.

We have two pieces of information:
1. The total number of tickets sold is 181.
   \[
   x + y = 181
   \]
2. The total money collected is $618. General tickets cost $4 and student tickets cost $3, so:
   \[
   4x + 3y = 618
   \]

We now have a system of equations:
\[
\begin{align*}
x + y &= 181 \quad \text{(1)} \\
4x + 3y &= 618 \quad \text{(2)}
\end{align*}
\]

### Solving the system of equations:

1. From equation (1), express $ y $ in terms of $ x $:
   \[
   y = 181 - x
   \]

2. Substitute this expression for $ y $ into equation (2):
   \[
   4x + 3(181 - x) = 618
   \]

3. Simplify and solve for $ x $:
   \[
   4x + 543 - 3x = 618
   \]
   \[
   x + 543 = 618
   \]
   \[
   x = 618 - 543
   \]
   \[
   x = 75
   \]

4. Now substitute $ x = 75 $ back into equation (1) to find $ y $:
   \[
   75 + y = 181
   \]
   \[
   y = 181 - 75
   \]
   \[
   y = 106
   \]

### Conclusion:
- 75 general admission tickets were sold.
- 106 student tickets were sold.

Would you like a further breakdown of any step or more details?

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Here are 5 related questions:
1. How can systems of equations be solved graphically?
2. What are some other methods to solve systems of equations, apart from substitution?
3. Can you solve a system of equations involving more than two variables?
4. What real-life situations can be modeled using systems of equations?
5. How would the solution change if general admission tickets were $5 instead?

**Tip:** When solving systems of equations, always check your solution by substituting values back into the original equations.

Tickets of a program at college cost $4 for general admission or $3 with a student ID. If 181 people paid to see a performance and $618 was collected, how many of each type of ticket were sold?

Learn how to solve a system of equations to find out how many general and student tickets were sold in a college program. This problem involves algebraic methods such as substitution and is suitable for students in Grades 7-10. The total revenue collected was $618, and 181 tickets were sold.

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