A high school principal is planning to start a new elective class. He randomly surveys 60 students to ask whether they would take the class, and 7 said they would. How many students can the principal expect to take the class if there are 540 students in the high school?
 
 
_____ students

This is a proportion problem. We can use the proportion of students who said they would take the class from the survey to estimate how many students out of the entire school population would take the class.

### Step 1: Set up the proportion
\[
\frac{7}{60} = \frac{x}{540}
\]
where:
- 7 is the number of students who said they would take the class,
- 60 is the total number of students surveyed,
- \(x\) is the expected number of students out of the total school population (540) who would take the class.

### Step 2: Solve for \(x\)
Cross-multiply to solve for \(x\):
\[
7 \times 540 = 60 \times x
\]
\[
3780 = 60x
\]
Now divide both sides by 60:
\[
x = \frac{3780}{60} = 63
\]

### Final Answer:
The principal can expect **63 students** to take the class.

Do you want any more details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you calculate proportions in other similar scenarios?
2. What are other ways to predict student interest based on a survey?
3. How does increasing the survey sample size affect prediction accuracy?
4. How could you adjust for survey bias in this type of problem?
5. What assumptions are made in this type of proportional reasoning?

**Tip:** In survey problems, ensure the sample is random to avoid bias affecting your predictions.

A high school principal is planning to start a new elective class. He randomly surveys 60 students to ask whether they would take the class, and 7 said they would. How many students can the principal expect to take the class if there are 540 students in the high school?

Learn how to estimate the number of students expected to take a new elective class using proportions. This example covers a survey of 60 students, where 7 said they would take the class, and helps predict the outcome for a total student body of 540. Suitable for students in Grades 6-8.

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