The school that Darryl goes to is selling tickets to the annual talent show. On the first day of ticket sales the school sold 200 student tickets and 25 adult tickets for a total of $2775. The school took in $3594 on the second day by selling 247 student tickets and 42 adult tickets.
What is the price each of one senior citizen ticket and one student ticket?

Let's denote the price of a student ticket by $ x $ dollars and the price of an adult ticket by $ y $ dollars. 

We are given two equations based on the ticket sales:

1. On the first day: 
   \[
   200x + 25y = 2775
   \]
2. On the second day: 
   \[
   247x + 42y = 3594
   \]

We can solve this system of linear equations to find the values of $ x $ and $ y $.

### Step 1: Solve the first equation for $ y $
\[
200x + 25y = 2775
\]
\[
25y = 2775 - 200x
\]
\[
y = \frac{2775 - 200x}{25}
\]
\[
y = 111 - 8x
\]

### Step 2: Substitute $ y = 111 - 8x $ into the second equation
\[
247x + 42(111 - 8x) = 3594
\]
\[
247x + 4662 - 336x = 3594
\]
\[
-89x + 4662 = 3594
\]
\[
-89x = 3594 - 4662
\]
\[
-89x = -1068
\]
\[
x = \frac{-1068}{-89} = 12
\]

### Step 3: Substitute $ x = 12 $ back into the equation for $ y $
\[
y = 111 - 8(12)
\]
\[
y = 111 - 96
\]
\[
y = 15
\]

### Final Answer:
- The price of a student ticket ($ x $) is **$12**.
- The price of an adult ticket ($ y $) is **$15**.

Would you like further details or have any questions?

---

**Related Questions:**

1. How would the system of equations change if the school sold different numbers of tickets?
2. What if the total earnings from the first day were $3000 instead?
3. How could you solve these equations graphically?
4. What happens if both tickets were priced the same?
5. How would you solve this problem using matrix methods?

**Tip:** When solving linear equations, isolating one variable first can simplify the process significantly.

Learn how to solve a system of linear equations to determine the price of student and adult tickets based on ticket sales data. This problem involves using the substitution method to find the values of variables. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation