3 Erasers Cost $\$ 4.41$. Which Equation Would Help Determine The Cost Of 4 Erasers?Choose 1 Answer:A. $\frac{4}{x}=\frac{\$ 4.41}{3}$B. $\frac{4}{\$ 4.41}=\frac{x}{3}$C. $\frac{4}{3}=\frac{\$ 4.41}{x}$D.

Understanding the Problem

In this problem, we are given the cost of 3 erasers, which is $\$ 4.41$. We need to determine the cost of 4 erasers using an equation. To solve this problem, we need to understand the concept of proportionality and how it can be applied to solve problems involving ratios and proportions.

Analyzing the Options

Let's analyze the given options to determine which equation would help us find the cost of 4 erasers.

Option A: $\frac{4}{x}=\frac{\$ 4.41}{3}$

This equation represents the ratio of the number of erasers to the cost of the erasers. However, it does not provide a direct relationship between the number of erasers and the cost of the erasers. Therefore, this equation is not suitable for solving the problem.

Option B: $\frac{4}{\$ 4.41}=\frac{x}{3}$

This equation represents the ratio of the number of erasers to the cost of the erasers, but it is not in the correct form to solve the problem. The cost of the erasers should be in the denominator, not the numerator.

Option C: $\frac{4}{3}=\frac{\$ 4.41}{x}$

This equation represents the ratio of the number of erasers to the cost of the erasers, with the cost of the erasers in the denominator. This is the correct form to solve the problem, as it allows us to find the cost of 4 erasers by multiplying the cost of 3 erasers by the ratio of the number of erasers.

Option D: (Not Provided)

Since option D is not provided, we will not consider it in our analysis.

Conclusion

Based on our analysis, the correct equation to determine the cost of 4 erasers is:

$\frac{4}{3}=\frac{\$ 4.41}{x}$

This equation represents the ratio of the number of erasers to the cost of the erasers, with the cost of the erasers in the denominator. By solving this equation, we can find the cost of 4 erasers.

Solving the Equation

To solve the equation, we can start by cross-multiplying:

$4x = 3 \times \$ 4.41$

$4x = \$ 13.23$

Next, we can divide both sides of the equation by 4 to find the value of x:

$x = \frac{\$ 13.23}{4}$

$x = \$ 3.3075$

Therefore, the cost of 4 erasers is approximately $\$ 13.23$.

Real-World Applications

This problem has real-world applications in various fields, such as business and finance. For example, a company that produces erasers may need to determine the cost of producing a certain number of erasers. By using the equation we derived, the company can calculate the cost of producing a larger quantity of erasers.

Conclusion

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Q: What is the concept of proportionality in mathematics?

A: Proportionality is a concept in mathematics that describes the relationship between two or more quantities that are directly or inversely proportional to each other. In the context of the problem, proportionality is used to describe the relationship between the number of erasers and the cost of the erasers.

Q: Why is it important to understand proportionality in mathematics?

A: Understanding proportionality is important in mathematics because it allows us to solve problems involving ratios and proportions. It is a fundamental concept in mathematics that has real-world applications in various fields, such as business and finance.

Q: How do I determine the cost of a larger quantity of erasers using the equation?

A: To determine the cost of a larger quantity of erasers using the equation, you can simply multiply the cost of the smaller quantity of erasers by the ratio of the larger quantity to the smaller quantity. For example, if you want to find the cost of 6 erasers, you can multiply the cost of 4 erasers by 6/4.

Q: What are some real-world applications of the concept of proportionality?

A: The concept of proportionality has real-world applications in various fields, such as business and finance. For example, a company that produces erasers may need to determine the cost of producing a certain number of erasers. By using the equation we derived, the company can calculate the cost of producing a larger quantity of erasers.

Q: How do I solve the equation $\frac{4}{3}=\frac{\$ 4.41}{x}$?

A: To solve the equation, you can start by cross-multiplying:

$4x = 3 \times \$ 4.41$

$4x = \$ 13.23$

Next, you can divide both sides of the equation by 4 to find the value of x:

$x = \frac{\$ 13.23}{4}$

$x = \$ 3.3075$

Therefore, the cost of 4 erasers is approximately $\$ 13.23$.

Q: What is the significance of the equation $\frac{4}{3}=\frac{\$ 4.41}{x}$?

A: The equation $\frac{4}{3}=\frac{\$ 4.41}{x}$ represents the ratio of the number of erasers to the cost of the erasers, with the cost of the erasers in the denominator. This equation is significant because it allows us to find the cost of a larger quantity of erasers by multiplying the cost of the smaller quantity of erasers by the ratio of the larger quantity to the smaller quantity.

Q: How do I apply the concept of proportionality to solve problems involving ratios and proportions?

A: To apply the concept of proportionality to solve problems involving ratios and proportions, you can follow these steps:

1. Identify the ratio or proportion that needs to be solved.
2. Write an equation that represents the ratio or proportion.
3. Solve the equation to find the value of the unknown quantity.
4. Use the value of the unknown quantity to solve the problem.

Q: What are some common mistakes to avoid when solving problems involving ratios and proportions?

A: Some common mistakes to avoid when solving problems involving ratios and proportions include:

• Not identifying the ratio or proportion that needs to be solved.
• Writing an equation that does not represent the ratio or proportion.
• Not solving the equation correctly.
• Not using the value of the unknown quantity to solve the problem.

Conclusion

In conclusion, the concept of proportionality is a fundamental concept in mathematics that has real-world applications in various fields, such as business and finance. By understanding proportionality, you can solve problems involving ratios and proportions, and apply the concept to solve real-world problems.