Tommy Buys Two Designer Shirts And Gets $$ 17$ Off The Total Price Of The Two Shirts. He Pays Exactly $$ 180$[/tex] For The Two Shirts With The Discount. Create An Equation That Could Be Used To Find The Price Of Each Shirt

Mar 13, 2025 by ADMIN 228 views

Tommy's Designer Shirts: A Math Problem

In this problem, we are given that Tommy buys two designer shirts and gets a discount of $17 on the total price of the two shirts. He pays exactly $180 for the two shirts with the discount. Our goal is to create an equation that could be used to find the price of each shirt.

Let's Break It Down

Let's denote the price of each shirt as x. Since Tommy buys two shirts, the total price of the two shirts is 2x. We are given that he gets a discount of $17 on the total price, so the discounted price is 2x - 17. We are also given that he pays exactly $180 for the two shirts with the discount.

Creating the Equation

We can now create an equation based on the information given. The equation is:

2x - 17 = 180

This equation represents the situation where the discounted price of the two shirts is equal to $180.

Solving the Equation

To solve the equation, we need to isolate the variable x. We can do this by adding 17 to both sides of the equation:

2x = 180 + 17 2x = 197

Next, we can divide both sides of the equation by 2 to solve for x:

x = 197 / 2 x = 98.5

Interpretation

So, the price of each shirt is $98.50. This means that each shirt costs $98.50, and the total price of the two shirts is $197.

In this problem, we created an equation to find the price of each shirt. We used the information given to set up the equation and then solved for the variable x. The solution to the equation gave us the price of each shirt, which is $98.50.

Example Use Case

This problem can be used to demonstrate the concept of creating and solving equations in a real-world scenario. It can also be used to practice solving linear equations and to understand the concept of discounts and prices.

Tips and Variations

To make the problem more challenging, you can add more variables or constraints.
To make the problem easier, you can provide more information or simplify the equation.
You can also use this problem to practice solving quadratic equations or systems of equations.

Mathematical Concepts

This problem involves the following mathematical concepts:

Linear equations
Solving for a variable
Discounts and prices
Algebraic manipulation

Real-World Applications

This problem has real-world applications in the following areas:

Retail and sales
Finance and accounting
Business and economics

In conclusion, this problem demonstrates the importance of creating and solving equations in a real-world scenario. It also highlights the need to understand mathematical concepts such as linear equations and algebraic manipulation. By practicing problems like this, you can develop your problem-solving skills and become more confident in your ability to solve mathematical equations.
Tommy's Designer Shirts: A Math Problem - Q&A

In our previous article, we created an equation to find the price of each shirt that Tommy bought. We solved the equation and found that the price of each shirt is $98.50. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the total price of the two shirts?

A: The total price of the two shirts is $197. This is the sum of the price of each shirt, which is $98.50.

Q: How much discount did Tommy get on the total price of the two shirts?

A: Tommy got a discount of $17 on the total price of the two shirts.

Q: What is the equation that represents the situation?

A: The equation that represents the situation is:

2x - 17 = 180

This equation represents the situation where the discounted price of the two shirts is equal to $180.

Q: How do I solve the equation?

A: To solve the equation, you need to isolate the variable x. You can do this by adding 17 to both sides of the equation:

2x = 180 + 17 2x = 197

Next, you can divide both sides of the equation by 2 to solve for x:

x = 197 / 2 x = 98.5

Q: What if I want to find the price of each shirt if the discount is $25 instead of $17?

A: If the discount is $25 instead of $17, you can create a new equation:

2x - 25 = 180

You can solve this equation by adding 25 to both sides of the equation:

2x = 180 + 25 2x = 205

Next, you can divide both sides of the equation by 2 to solve for x:

x = 205 / 2 x = 102.5

Q: Can I use this problem to practice solving quadratic equations?

A: Yes, you can use this problem to practice solving quadratic equations. For example, if the discount is $25 instead of $17, you can create a quadratic equation:

2x^2 - 25x - 180 = 0

You can solve this equation using the quadratic formula or factoring.

Q: What are some real-world applications of this problem?

A: This problem has real-world applications in the following areas:

Retail and sales: You can use this problem to calculate the price of items after a discount.
Finance and accounting: You can use this problem to calculate the cost of goods sold or the revenue from sales.
Business and economics: You can use this problem to analyze the impact of discounts on sales or revenue.

Q: What is the total price of the two shirts?
A: The total price of the two shirts is $197.
Q: How much discount did Tommy get on the total price of the two shirts?
A: Tommy got a discount of $17 on the total price of the two shirts.
Q: What is the equation that represents the situation?
A: The equation that represents the situation is 2x - 17 = 180.
Q: How do I solve the equation?
A: To solve the equation, you need to isolate the variable x by adding 17 to both sides of the equation and then dividing both sides by 2.

Mathematical Concepts

This problem involves the following mathematical concepts:

Linear equations
Solving for a variable
Discounts and prices
Algebraic manipulation
Quadratic equations

Real-World Applications

This problem has real-world applications in the following areas:

Retail and sales
Finance and accounting
Business and economics