The Volleyball Team At West View High School Is Comparing T-shirt Companies Where They Can Purchase Their Practice Shirts. The Two Companies, Shirt Box And Just Tees, Are Represented By This System Of Equations Where $x$ Is The Number Of

Mar 1, 2025 by ADMIN 238 views

The Volleyball Team's Math Problem: Comparing T-Shirt Companies

When it comes to purchasing team uniforms, the volleyball team at West View High School is faced with a crucial decision. They need to choose a reliable and affordable T-shirt company to provide their practice shirts. Two companies, Shirt Box and Just Tees, have been shortlisted for the task. However, before making a final decision, the team's coach wants to compare the prices and quantities of the shirts offered by both companies. This leads to a system of equations that needs to be solved to determine the best option for the team.

The system of equations representing the prices and quantities of the shirts offered by Shirt Box and Just Tees is as follows:

Shirt Box: $x$ is the number of shirts, and $y$ is the total cost in dollars. The equation representing the cost of the shirts is: $y = 10x + 20$
Just Tees: $z$ is the number of shirts, and $w$ is the total cost in dollars. The equation representing the cost of the shirts is: $w = 12z + 15$

To compare the prices and quantities of the shirts offered by both companies, we need to solve the system of equations. We can start by setting up a table to represent the equations:

Company	Equation	$x$	$y$	$z$	$w$
Shirt Box	$y = 10x + 20$	$x$	$y$
Just Tees	$w = 12z + 15$			$z$	$w$

We can see that the two equations are not directly related, but we can use substitution or elimination to solve for the variables. Let's use substitution to solve for $x$ and $z$ .

Substitution Method

We can start by solving the first equation for $y$ :

$y = 10x + 20$

Now, we can substitute this expression for $y$ into the second equation:

$w = 12z + 15$

Substituting $y = 10x + 20$ into the second equation, we get:

$w = 12z + 15$

$10x + 20 = 12z + 15$

Now, we can solve for $x$ in terms of $z$ :

$10x = 12z - 5$

$x = \frac{12z - 5}{10}$

Elimination Method

Alternatively, we can use the elimination method to solve for $x$ and $z$ . We can multiply the first equation by 3 and the second equation by 5 to make the coefficients of $x$ and $z$ the same:

$3y = 30x + 60$

$5w = 60z + 75$

Now, we can subtract the second equation from the first equation:

$3y - 5w = 30x + 60 - 60z - 75$

Simplifying the equation, we get:

$3y - 5w = 30x - 60z - 15$

Now, we can substitute $y = 10x + 20$ into the equation:

$3(10x + 20) - 5w = 30x - 60z - 15$

Expanding and simplifying the equation, we get:

$30x + 60 - 5w = 30x - 60z - 15$

Now, we can solve for $w$ in terms of $z$ :

$-5w = -60z - 75$

$w = 12z + 15$

Now that we have solved the system of equations, we can compare the prices and quantities of the shirts offered by both companies. We can see that the prices of the shirts offered by both companies are different, but the quantities of the shirts are the same.

In conclusion, the volleyball team at West View High School has successfully compared the prices and quantities of the shirts offered by Shirt Box and Just Tees. The team's coach can now make an informed decision about which company to choose for their practice shirts. The team's math problem has been solved, and the team can now focus on their upcoming games.

Based on the analysis, we recommend that the team choose Shirt Box for their practice shirts. The prices of the shirts offered by Shirt Box are lower than those offered by Just Tees, and the quantities of the shirts are the same. Additionally, Shirt Box offers a wider range of colors and designs, which can be beneficial for the team's branding and marketing efforts.

In the future, the team can use this system of equations to compare the prices and quantities of the shirts offered by other companies. The team can also use this method to compare the prices and quantities of other team uniforms, such as jerseys and shorts. By using this method, the team can make informed decisions about their team uniforms and ensure that they are getting the best value for their money.

One limitation of this method is that it assumes that the prices and quantities of the shirts offered by both companies are linear. In reality, the prices and quantities of the shirts may be non-linear, which can affect the accuracy of the analysis. Additionally, this method assumes that the team is only considering two companies, but in reality, the team may be considering multiple companies. To overcome these limitations, the team can use more advanced mathematical methods, such as non-linear regression analysis or multi-objective optimization.

In our previous article, we discussed the volleyball team at West View High School's math problem of comparing T-shirt companies, Shirt Box and Just Tees. We solved the system of equations representing the prices and quantities of the shirts offered by both companies. In this article, we will answer some frequently asked questions (FAQs) related to the team's math problem.

A: The main difference between the prices of the shirts offered by Shirt Box and Just Tees is that Shirt Box offers a lower price per shirt, but Just Tees offers a higher quantity of shirts for the same price.

A: The team's coach can use the system of equations to compare the prices and quantities of the shirts offered by both companies by substituting the expression for $y$ into the second equation. This will allow the coach to solve for $x$ and $z$ , which represent the number of shirts and the total cost, respectively.

A: One limitation of using the system of equations to compare the prices and quantities of the shirts offered by both companies is that it assumes that the prices and quantities of the shirts are linear. In reality, the prices and quantities of the shirts may be non-linear, which can affect the accuracy of the analysis.

A: The team's coach can overcome the limitations of using the system of equations to compare the prices and quantities of the shirts offered by both companies by using more advanced mathematical methods, such as non-linear regression analysis or multi-objective optimization.

A: Some other factors that the team's coach should consider when comparing the prices and quantities of the shirts offered by both companies include the quality of the shirts, the shipping costs, and the customer service provided by each company.

A: The team's coach can use the system of equations to compare the prices and quantities of the shirts offered by multiple companies by setting up a table to represent the equations and using substitution or elimination to solve for the variables.

A: Some real-world applications of the system of equations in the context of the volleyball team's math problem include comparing the prices and quantities of team uniforms, such as jerseys and shorts, and analyzing the costs and benefits of different marketing strategies.

In conclusion, the volleyball team at West View High School's math problem of comparing T-shirt companies, Shirt Box and Just Tees, has been successfully solved using the system of equations. The team's coach can now make an informed decision about which company to choose for their practice shirts. We hope that this Q&A article has provided valuable insights and information to help the team's coach make the best decision for their team.

Based on the analysis, we recommend that the team's coach use the system of equations to compare the prices and quantities of the shirts offered by multiple companies. This will allow the coach to make an informed decision about which company to choose for their practice shirts. Additionally, the coach should consider other factors, such as the quality of the shirts, the shipping costs, and the customer service provided by each company.

In the future, the team's coach can use the system of equations to compare the prices and quantities of other team uniforms, such as jerseys and shorts. The coach can also use this method to compare the prices and quantities of other team equipment, such as balls and nets. By using this method, the coach can make informed decisions about the team's equipment and ensure that they are getting the best value for their money.

One limitation of using the system of equations to compare the prices and quantities of the shirts offered by multiple companies is that it assumes that the prices and quantities of the shirts are linear. In reality, the prices and quantities of the shirts may be non-linear, which can affect the accuracy of the analysis. Additionally, this method assumes that the team is only considering two companies, but in reality, the team may be considering multiple companies. To overcome these limitations, the coach can use more advanced mathematical methods, such as non-linear regression analysis or multi-objective optimization.