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.