Mathematical Problem Solving: Finding the Price of an Adult Ticket at a School Carnival

In this article, we will solve a practical algebra problem to determine the price of an adult ticket at a school carnival using the given payment information for two individuals, Tommie and Susan. Understanding how to solve such problems is essential for various professions, including SEO, as it can help in creating engaging and informative content that users find valuable.

Context and Problem Statement

Imagine a school carnival where ticket prices are unknown but can be deduced from the payment information of two individuals, Tommie and Susan. The goal is to determine the price of an adult ticket given the total cost of different combinations of tickets bought by Tommie and Susan. This type of problem is a common application of algebra in real-world scenarios, making it a perfect exercise for students and professionals alike to improve their problem-solving skills.

Variables and Equations

To solve this problem, we first define our variables: x - the cost of one youth ticket y - the cost of one adult ticket Based on the given information, we can set up the following equations:

1. Tommie's Purchase: 6 youth tickets and 1 adult ticket cost $17.50

[6x y 17.50] -- Eq.1

2. Susan's Purchase: 3 youth tickets and 3 adult tickets cost $22.50

[3x 3y 22.50] -- Eq.2

Solving the Equations

Our next step is to manipulate these equations to solve for y, the cost of an adult ticket. We start by simplifying Eq.2.

Eq.2 can be divided by 3:

[frac{3x 3y}{3} frac{22.50}{3}]

[x y 7.50] -- Eq.3

Now, we subtract Eq.1 from Eq.3:

[(x y) - (6x y) 7.50 - 17.50]

[7.50 - 6x - y -10.00]

[5x 10.00]

[x 2.00]

Since we already have the equation (x y 7.50) and we just solved for (x 2.00), we can substitute (x) back into the equation:

[2 y 7.50]

[y 5.50]

Hence, the cost of an adult ticket is $5.50.

Conclusion and Application

This problem-solving technique can be applied in various real-world scenarios, such as calculating the cost of goods in a store, determining price variations in different markets, or even in SEO content optimization, where understanding user behavior and price sensitivity can lead to more effective marketing strategies. By mastering such mathematical problems, individuals can enhance their analytical skills, which are essential in today's data-driven world.

Additional Tips for SEO and Content Creation

When creating content or optimizing SEO, always ensure the content aligns with the keywords and answers the questions your target audience might have. Incorporating practical problem-solving examples in your articles can make the content more engaging and provide value to your readers. For instance, using examples like this algebra problem can help readers connect to the content emotionally and intellectually, making them more likely to share and engage with your posts.

Keywords: adult ticket, youth ticket, carnival tickets, price calculation, algebra problem