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In order to decide how to market a new line of clothing, Mary is researching the demographics of the customers at 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

Week & 1 & 2 & 3 & 4 \\

\hline

Customers & 2,848 & 3,141 & 3,861 & 3,911 \\

\hline

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.
- Multiply the predicted number of customers by the average ratio to estimate the number of students.
- Round the result to the nearest whole number, so the final answer is $\boxed{2446}$.

### Explanation
1. Problem Analysis
We are given the number of customers and high school students for four weeks and asked to predict the number of high school students for the next week, given the number of customers. We will calculate the ratio of students to customers for each week, then find the average of these ratios. Finally, we will multiply the predicted number of customers by the average ratio to estimate the number of students.

2. Calculating Ratios
First, calculate the student to customer ratio for each week:
Week 1: $r_1 = \frac{2033}{2848} \approx 0.7138$
Week 2: $r_2 = \frac{1937}{3141} \approx 0.6167$
Week 3: $r_3 = \frac{2076}{3861} \approx 0.5377$
Week 4: $r_4 = \frac{1721}{3911} \approx 0.4400$

3. Finding the Average Ratio
Next, calculate the average student to customer ratio:
$r_{avg} = \frac{0.7138 + 0.6167 + 0.5377 + 0.4400}{4} = \frac{2.3082}{4} \approx 0.5771$

4. Estimating the Number of Students
Now, multiply the predicted number of customers next week by the average ratio to estimate the number of students:
$students = 4238 \times 0.5771 \approx 2445.58$

5. Final Answer
Finally, round the result to the nearest whole number: $2445.58 \approx 2446$. Therefore, the store should expect approximately 2446 high school students next week.

### Examples
Understanding customer demographics is crucial for tailoring marketing strategies. For instance, if a store knows that a significant portion of its customers are high school students, it can adjust its inventory to include more trendy and affordable clothing options. Similarly, marketing campaigns can be designed to appeal to this specific demographic, potentially increasing sales and customer loyalty. This type of analysis is also useful for staffing decisions, ensuring that there are enough employees available during peak hours for student customers.

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