A Company Sold 3,000 Computers In One Month, But 12 Were Returned. If 3,500 Were Sold The Next Month, The Company Would Expect 14 To Be Returned.What Is A Valid Proportion To Represent The Problem?A. 3 , 000 12 = 14 3 , 500 \frac{3,000}{12}=\frac{14}{3,500} 12 3 , 000 ​ = 3 , 500 14 ​ B.

Understanding the Problem

The problem presents a scenario where a company sells a certain number of computers in two consecutive months and experiences returns in both periods. We are given that the company sold 3,000 computers in the first month and 12 were returned. In the second month, the company sold 3,500 computers and would expect 14 to be returned. Our goal is to find a valid proportion that represents this problem.

Identifying the Key Elements

To establish a valid proportion, we need to identify the key elements involved in the problem. These elements include the number of computers sold, the number of returns, and the expected returns in the second month.

Number of Computers Sold

• First month: 3,000 computers
• Second month: 3,500 computers

Number of Returns

• First month: 12 returns
• Second month: 14 expected returns

Establishing the Proportion

A proportion is a statement that two ratios are equal. In this case, we can establish a proportion by comparing the number of returns to the number of computers sold in both months.

Option A: $\frac{3,000}{12}=\frac{14}{3,500}$

This option presents a proportion that compares the number of returns to the number of computers sold in both months. However, we need to verify whether this proportion accurately represents the problem.

Verifying the Proportion

To verify the proportion, we can cross-multiply and check if the resulting equation is true.

$\frac{3,000}{12}=\frac{14}{3,500}$

Cross-multiplying:

$3,000 \cdot 3,500 = 12 \cdot 14$

$10,500,000 = 168$

The resulting equation is not true, which means that option A is not a valid proportion to represent the problem.

Conclusion

Based on the analysis, we can conclude that the proportion $\frac{3,000}{12}=\frac{14}{3,500}$ is not a valid representation of the problem. However, we can establish a valid proportion by comparing the number of returns to the number of computers sold in both months.

A Valid Proportion

A valid proportion can be established by comparing the number of returns to the number of computers sold in both months. We can use the following proportion:

$\frac{12}{3,000}=\frac{14}{3,500}$

This proportion accurately represents the problem and can be used to solve for the expected returns in the second month.

Final Answer

The final answer is: $\boxed{\frac{12}{3,000}=\frac{14}{3,500}}$

Understanding the Problem

The problem presents a scenario where a company sells a certain number of computers in two consecutive months and experiences returns in both periods. We are given that the company sold 3,000 computers in the first month and 12 were returned. In the second month, the company sold 3,500 computers and would expect 14 to be returned. Our goal is to find a valid proportion that represents this problem.

Q&A

Q: What is a proportion in mathematics?

A: A proportion is a statement that two ratios are equal. It is a way to compare two different quantities by setting up a mathematical equation.

Q: How do we establish a proportion in this problem?

A: To establish a proportion, we need to identify the key elements involved in the problem, which include the number of computers sold, the number of returns, and the expected returns in the second month. We can then compare these elements to set up a proportion.

Q: What is the correct proportion to represent the problem?

A: The correct proportion to represent the problem is:

$\frac{12}{3,000}=\frac{14}{3,500}$

This proportion accurately represents the problem and can be used to solve for the expected returns in the second month.

Q: Why is the proportion $\frac{3,000}{12}=\frac{14}{3,500}$ not valid?

A: The proportion $\frac{3,000}{12}=\frac{14}{3,500}$ is not valid because it does not accurately represent the problem. When we cross-multiply, we get $10,500,000 = 168$, which is not true.

Q: What is the significance of the proportion in this problem?

A: The proportion is significant because it allows us to compare the number of returns to the number of computers sold in both months. This comparison helps us to understand the relationship between the number of returns and the number of computers sold.

Q: How can we use the proportion to solve for the expected returns in the second month?

A: We can use the proportion to solve for the expected returns in the second month by setting up an equation based on the proportion. For example, if we want to find the expected returns in the second month, we can set up the equation:

$\frac{12}{3,000}=\frac{x}{3,500}$

where x is the expected returns in the second month. We can then solve for x by cross-multiplying and simplifying the equation.

Conclusion

In conclusion, the proportion $\frac{12}{3,000}=\frac{14}{3,500}$ is a valid representation of the problem. It accurately compares the number of returns to the number of computers sold in both months and can be used to solve for the expected returns in the second month.

Final Answer

The final answer is: $\boxed{\frac{12}{3,000}=\frac{14}{3,500}}$