Nichole's school is selling tickets to a chorus concert.  On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38.  On the second day of ticket sales, the school sold another 3 senior citizen tickets and 2 child tickets for $52.



Let's define the variables for the problem:

- Let **S** represent the price of one senior citizen ticket.
- Let **C** represent the price of one child ticket.

From the problem, we can set up the following system of equations based on the ticket sales:

1. For the first day:  
   $ 3S + 1C = 38 $  
   (The school sold 3 senior citizen tickets and 1 child ticket for $38.)

2. For the second day:  
   $ 3S + 2C = 52 $  
   (The school sold 3 senior citizen tickets and 2 child tickets for $52.)

Now, we can solve this system of equations to find the values of $ S $ and $ C $.

### Step 1: Subtract the first equation from the second to eliminate $ S $.

\[
(3S + 2C) - (3S + 1C) = 52 - 38
\]

Simplifying this:

\[
C = 14
\]

### Step 2: Substitute $ C = 14 $ into the first equation to solve for $ S $.

\[
3S + 1(14) = 38
\]

\[
3S + 14 = 38
\]

\[
3S = 38 - 14
\]

\[
3S = 24
\]

\[
S = \frac{24}{3} = 8
\]

### Final Answer:
- The price of a senior citizen ticket is **$8**.
- The price of a child ticket is **$14**.

Do you want more details or have any questions?  

Here are 5 related questions:
1. How would the system change if the ticket prices were different?
2. What if the number of tickets sold was higher on both days?
3. Can you find a method to solve the system graphically?
4. How would the problem change if Nichole's school offered a discount on senior tickets?
5. Can you model a scenario where adult tickets are sold along with senior and child tickets?

**Tip:** To solve systems of equations, elimination is often quicker when coefficients for one variable are the same across the equations.

Nichole's school is selling tickets to a chorus concert. On the first day of ticket sales, the school sold 3 senior citizen tickets and 1 child ticket for a total of $38. On the second day of ticket sales, the school sold another 3 senior citizen tickets and 2 child tickets for $52.

Learn how to solve a system of equations for determining senior and child ticket prices based on a school's chorus concert sales. This problem covers key algebraic concepts such as systems of linear equations, suitable for students in Grades 7-9. Step-by-step solution included.

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