Equations to Find the Price of the Tire Patches

Oct 13, 2025 by leolavanderia.com.br 92 views

Introduction

Rhyan, an avid mountain biker, recently purchased four tire patches to prepare for his upcoming trip. To pay for the tire patches, he used a gift card that had a balance of $\$22.20$ . After the transaction, the gift card had a remaining balance of $\$1.90$ . In this article, we will explore the mathematical equations that can be used to find the price of the four tire patches.

Understanding the Problem

Let's denote the price of one tire patch as $x$ . Since Rhyan bought four tire patches, the total cost of the tire patches is $4x$ . We know that Rhyan's gift card had a balance of $\$22.20$ before the transaction and $\$1.90$ after the transaction. This means that the total cost of the tire patches is the difference between the initial and final balances of the gift card.

Equations to Find the Price of the Tire Patches

There are two equations that can be used to find the price of the tire patches:

Equation 1: Subtracting the Final Balance from the Initial Balance

The first equation is based on the fact that the total cost of the tire patches is the difference between the initial and final balances of the gift card.

22.20 - 1.90 = 4x

Simplifying the equation, we get:

20.30 = 4x

Equation 2: Dividing the Difference by 4

The second equation is based on the fact that the total cost of the tire patches is equal to the difference between the initial and final balances of the gift card divided by 4.

\frac{22.20 - 1.90}{4} = x

Simplifying the equation, we get:

\frac{20.30}{4} = x

Solving for x

To find the price of one tire patch, we can solve for x in either equation.

Solving Equation 1

20.30 = 4x

Dividing both sides by 4, we get:

x = \frac{20.30}{4}

Simplifying, we get:

x = 5.075

Solving Equation 2

\frac{22.20 - 1.90}{4} = x

Simplifying, we get:

\frac{20.30}{4} = x

Simplifying, we get:

x = 5.075

Conclusion

$In this article, we explored the mathematical equations that can be used to find the price of the four tire patches that Rhyan bought to prepare for his mountain biking trip. We used two equations to find the price of one tire patch, and both equations yielded the same result: $x = 5.075$. This means that the price of one tire patch is $\$5.08$.<br/> **To Prepare for His Mountain Biking Trip, Rhyan Bought Four Tire Patches: A Mathematical Approach**$

Q&A: Frequently Asked Questions

Q: What is the problem about? A: The problem is about Rhyan, a mountain biker, who bought four tire patches using a gift card that had a balance of $\$22.20$ . After the transaction, the gift card had a remaining balance of $\$1.90$ . We need to find the price of one tire patch.

Q: What are the two equations that can be used to find the price of the tire patches? A: The two equations are:

$22.20 - 1.90 = 4x$
$\frac{22.20 - 1.90}{4} = x$

Q: How do we simplify the first equation? A: To simplify the first equation, we subtract $1.90$ from $22.20$ to get $20.30$ . Then, we divide both sides of the equation by $4$ to get $x = \frac{20.30}{4}$ .

Q: How do we simplify the second equation? A: To simplify the second equation, we subtract $1.90$ from $22.20$ to get $20.30$ . Then, we divide the result by $4$ to get $x = \frac{20.30}{4}$ .

Q: What is the value of x? A: The value of x is $5.075$ , which means that the price of one tire patch is $\$5.08$ .

Q: Why do we need to find the price of one tire patch? A: We need to find the price of one tire patch to determine the total cost of the four tire patches that Rhyan bought.

Q: What is the total cost of the four tire patches? A: The total cost of the four tire patches is $4x$ , where x is the price of one tire patch. Since x is $5.075$ , the total cost of the four tire patches is $4 \times 5.075 = 20.30$ .

Q: What is the remaining balance of the gift card after the transaction? A: The remaining balance of the gift card after the transaction is $\$1.90$ .

Q: What is the initial balance of the gift card before the transaction? A: The initial balance of the gift card before the transaction is $\$22.20$ .

Q: How do we find the price of the tire patches using the initial and final balances of the gift card? A: We find the price of the tire patches by subtracting the final balance from the initial balance and dividing the result by $4$ .

Q: What is the relationship between the initial and final balances of the gift card and the price of the tire patches? A: The initial balance of the gift card is equal to the final balance plus the total cost of the tire patches. In other words, $22.20 = 1.90 + 4x$ .