Solving Real-World Problems with Equations: The School Play Ticket Sale

Ever faced a problem that seems too complex to solve at first glance? Don’t worry; often, these problems can be tackled by breaking them down into smaller, more manageable parts. In this article, we will explore a real-world example involving ticket sales for a school play, and show you how to use algebra to find the solution easily.

The Problem: Ticket Sales for the School Play

A school is hosting a play and has sold a total of 320 tickets. The problem is further complicated by the fact that the number of student tickets sold is three times the number of adult tickets sold. How can we determine the exact number of tickets sold for each category?

Solving the Problem with Equations

Step 1: Defining Variables

Let's start by defining our variables. We can use the letter ( x ) to represent the number of adult tickets sold. Since the number of student tickets sold is three times the number of adult tickets, we can represent the number of student tickets as ( 3x ).

Step 2: Setting Up the Equation

The total number of tickets sold is the sum of adult and student tickets, which is given as 320. Therefore, we can set up the equation:

x 3x 320

Step 3: Solving the Equation

Now we simplify and solve the equation:

4x 320

To solve for ( x ):

x frac{320}{4} 80

This means that 80 adult tickets were sold.

Step 4: Finding the Number of Student Tickets

Since the number of student tickets is three times the number of adult tickets:

3x 3 times 80 240

Therefore, 240 student tickets were sold.

Summary of the Solution

The number of adult tickets sold: 80 The number of student tickets sold: 240

Final Equation

The equation we used was:

x 3x 320, where ( x ) is the number of adult tickets.

Conclusion

In this article, we demonstrated how to use algebraic equations to solve a real-world problem involving ticket sales for a school play. By breaking down the problem into manageable steps and using algebraic methods, we were able to find the exact number of tickets sold for each category. This technique can be applied to many other real-world problems where variables and equations play a crucial role.

Additional Information and Resources

For more practice and resources on solving word problems and using algebra, consider exploring additional materials on Khan Academy or Math is Fun.