In a survey, 40% of the respondents were satisfied with a service, and 30% of the satisfied respondents were also willing to recommend it. If 600 respondents were surveyed, how many people were both satisfied and willing to recommend the service?

Let's solve this problem step-by-step to find the number of people who were both satisfied and willing to recommend the service.

### Step-by-Step Solution

1. **Find the number of satisfied respondents:**

   Given that 40% of the respondents were satisfied with the service, and there were 600 respondents in total, the number of satisfied respondents can be calculated as:

   \[
   \text{Number of satisfied respondents} = 40\% \times 600 = 0.4 \times 600
   \]

   \[
   \text{Number of satisfied respondents} = 240
   \]

2. **Find the number of satisfied respondents who were willing to recommend the service:**

   It's given that 30% of the satisfied respondents were willing to recommend the service. So, we calculate 30% of the 240 satisfied respondents:

   \[
   \text{Number of respondents willing to recommend} = 30\% \times 240 = 0.3 \times 240
   \]

   \[
   \text{Number of respondents willing to recommend} = 72
   \]

### Conclusion

**72 respondents were both satisfied with the service and willing to recommend it.**

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What percentage of the total respondents were both satisfied and willing to recommend the service?
2. If 50% of the respondents who were not satisfied were also unwilling to recommend the service, how many respondents does this represent?
3. How many respondents were either satisfied or willing to recommend the service, but not both?
4. If the number of respondents increased to 1,200, how many would be both satisfied and willing to recommend the service?
5. What would be the number of respondents willing to recommend if the percentage of satisfied respondents who are willing to recommend increased to 50%?

**Tip**: When dealing with percentages in problems like this, convert them to decimals to simplify multiplication and division operations.

Explore a survey analysis problem involving percentages to determine satisfaction and recommendation rates. Learn how to calculate the number of respondents satisfied with a service and willing to recommend it. Suitable for high school students and those interested in survey data analysis.

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