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In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store. She counted the number of customers who visited the store over the course of a month and found out how many of the customers were high school students. Her collected data is in the table below.

\[
\begin{tabular}{|c|c|c|c|c|}
\hline
\text{Week} & 1 & 2 & 3 & 4 \\
\hline
\text{Customers} & 2,848 & 3,141 & 3,861 & 3,911 \\
\hline
\text{Students} & 2,033 & 1,937 & 2,076 & 1,721 \\
\hline
\end{tabular}
\]

Mary predicts that the store will see 4,238 customers next week. Approximately how many high school students should the store expect next week?

A. 1,865
B. 2,392
C. 2,446
D. 3,025

Answer :

- Calculate the student to customer ratio for each week.
- Calculate the average student to customer ratio over the four weeks: $\approx 0.5771$.
- Multiply the predicted number of customers next week by the average ratio: $4238 \times 0.5771 \approx 2445.58$.
- Round the result to the nearest whole number: $\boxed{2446}$.

### Explanation
1. Calculate Student to Customer Ratios
First, we need to calculate the ratio of students to customers for each week. This will help us understand the proportion of students visiting the store each week.

2. Week 1 Ratio
Week 1: The ratio of students to customers is $\frac{2033}{2848} \approx 0.7138$.

3. Week 2 Ratio
Week 2: The ratio of students to customers is $\frac{1937}{3141} \approx 0.6167$.

4. Week 3 Ratio
Week 3: The ratio of students to customers is $\frac{2076}{3861} \approx 0.5377$.

5. Week 4 Ratio
Week 4: The ratio of students to customers is $\frac{1721}{3911} \approx 0.4400$.

6. Calculate Average Ratio
Next, we calculate the average student to customer ratio over the four weeks. This will give us a general idea of the proportion of students visiting the store. The average ratio is $\frac{0.7138 + 0.6167 + 0.5377 + 0.4400}{4} \approx 0.5771$.

7. Predict Number of Students
Now, we use the average ratio to predict the number of students expected next week, given that the store expects 4,238 customers. We multiply the predicted number of customers by the average ratio: $4238 \times 0.5771 \approx 2445.58$.

8. Round to Nearest Whole Number
Finally, we round the predicted number of students to the nearest whole number, which is 2446.

9. Final Answer
Therefore, the store should expect approximately 2446 high school students next week.

### Examples
Understanding customer demographics, like the proportion of high school students, is crucial for tailoring marketing strategies. For instance, a clothing store can use this information to decide what type of clothing to promote or how to allocate marketing resources. If a significant portion of customers are high school students, the store might focus on promoting trendy and affordable clothing lines that appeal to this demographic. This targeted approach can lead to increased sales and customer satisfaction.

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Rewritten by : Barada