High School

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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.

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

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 ratio of students to customers for each week.
- Find the average of these ratios.
- Multiply the predicted number of customers by the average ratio to estimate the number of students.
- Round the result to the nearest whole number: $\boxed{2446}$.

### Explanation
1. Problem Analysis
We are given the number of customers and high school students who visited a clothing store over four weeks. Mary predicts the number of customers for the next week and wants to estimate the number of high school students expected next week. To do this, we will calculate the ratio of students to customers for each week, find the average of these ratios, and then multiply the predicted number of customers by this average ratio.

2. Calculating Ratios
First, we calculate the ratio of students to customers 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, we find the average of these ratios:
$\bar{r} = \frac{0.7138 + 0.6167 + 0.5377 + 0.4400}{4} = \frac{2.3082}{4} \approx 0.5771$

4. Estimating the Number of Students
Now, we multiply the predicted number of customers next week (4238) by the average ratio to estimate the number of students:
$S = 4238 \times 0.5771 \approx 2446.0598$

5. Final Answer
Finally, we round the result to the nearest whole number, which gives us 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. This kind of analysis helps businesses make informed decisions about their target audience and optimize their sales and marketing efforts.

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Rewritten by : Barada