Exploring the Unknown: A Math Problem in the Context of a Movie Theater Sales Scenario

Introduction

Dealing with ticket sales involves basic mathematics and can be a prime example to understand fundamental concepts of ratios and problem-solving. This article demonstrates how to calculate the number of children’s and adult tickets sold at a movie theater, given a particular ratio and total ticket sales.

The Problem

At a movie theater, the number of children’s tickets sold to an afternoon show was 5 times the number of adult tickets. The total number of tickets sold was 132. The goal is to determine the number of children’s tickets sold.

Mathematical Representation

To solve this problem, we can use variables to represent the quantities involved. Let:

C number of children’s tickets A number of adult tickets

The problem states that the number of children’s tickets is 5 times the number of adult tickets. This relationship can be written as:

C 5A

Additionally, the total number of tickets sold is 132. Therefore, we can express the total as:

C A 132

Solving the Equations

Step 1: Substitute the Relationship into the Total Equation

Since C 5A, we can substitute this into the total equation:

5A A 132

This simplifies to:

6A 132

Step 2: Solve for A

Divide both sides of the equation by 6:

A 22

Step 3: Determine the Number of Children’s Tickets

Now that we know A 22, we can find C using the relationship C 5A:

C 5 * 22 110

Verification

Let's verify the solution:

Number of adult tickets (A) 22 Number of children’s tickets (C) 110 Total tickets A C 22 110 132

The calculations are accurate, confirming our solution.

Additional Insight: Algebraic Solution

Alternatively, the problem can be approached using an algebraic formulation. Let x be the number of adult tickets. Then:

Total number of tickets sold x 5x 132 6x 132 x 22 Hence, number of children’s tickets 5x 5 * 22 110

Conclusion

This problem demonstrates the application of basic algebraic techniques to solve real-world scenarios in the context of ticket sales. Understanding these methods enhances problem-solving skills and can be applied in various situations.