A school is selling tickets to a spring musical. on the first day of ticket sales the school sold 11 senior citizen tickets and 7 child tickets for a total $146 on the second day by selling 14 senior citizen tickets and 6 child tickets. what price of one senior citizen tickets and one child ticket

Let's define variables to represent the prices of the tickets:

- Let $ x $ be the price of one senior citizen ticket.
- Let $ y $ be the price of one child ticket.

From the information given:

1. On the first day, the school sold 11 senior citizen tickets and 7 child tickets for a total of $146. This gives us the equation:
   \[
   11x + 7y = 146
   \]
2. On the second day, the school sold 14 senior citizen tickets and 6 child tickets for a total of $186. This gives us the equation:
   \[
   14x + 6y = 186
   \]

Now we have a system of linear equations:

1. $ 11x + 7y = 146 $
2. $ 14x + 6y = 186 $

### Solving the system:
We can solve this system using the elimination or substitution method. Here, let's use elimination.

**Step 1**: Multiply the first equation by 2 and the second equation by 1 to align the coefficients of $ y $:

\[
22x + 14y = 292 \quad \text{(Equation 1 multiplied by 2)}
\]
\[
14x + 6y = 186 \quad \text{(Equation 2 unchanged)}
\]

**Step 2**: Subtract the second equation from the first:

\[
(22x + 14y) - (14x + 6y) = 292 - 186
\]
\[
(22x - 14x) + (14y - 6y) = 106
\]
\[
8x + 8y = 106
\]
\[
8x = 106
\]
\[
x = \frac{106}{8} = 13.25
\]

So, the price of one senior citizen ticket is $ x = 13.25 $.

**Step 3**: Substitute $ x = 13.25 $ into the first equation to find $ y $:

\[
11(13.25) + 7y = 146
\]
\[
145.75 + 7y = 146
\]
\[
7y = 146 - 145.75
\]
\[
7y = 0.25
\]
\[
y = \frac{0.25}{7} = 0.0357
\]

So, the price of one child ticket is approximately $ y = 0.04 $ (or 4 cents).

### Final Answer:
- The price of one senior citizen ticket is $13.25.
- The price of one child ticket is approximately $0.04.

Would you like more details, or do you have any questions?

Here are five related questions to deepen understanding:

1. What is another method to solve this system of equations?
2. How can we check if the solution is correct?
3. What would happen if the prices of tickets changed after both days?
4. How would the solution differ if the number of tickets sold were swapped?
5. How can we generalize this process for other real-life scenarios?

**Tip:** When solving systems of equations, always double-check by substituting your solution into both original equations to ensure accuracy.

A school is selling tickets to a spring musical. On the first day of ticket sales, the school sold 11 senior citizen tickets and 7 child tickets for a total of $146. On the second day, they sold 14 senior citizen tickets and 6 child tickets for a total of $186. What is the price of one senior citizen ticket and one child ticket?

Learn how to determine ticket prices for senior citizens and children from a system of equations based on two days of ticket sales for a spring musical. This solution includes step-by-step guidance using elimination and substitution methods, ideal for students in Grades 8-10.

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