Math Problem Statement
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?
Solution
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
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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:
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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:
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:
- What percentage of the total respondents were both satisfied and willing to recommend the service?
- If 50% of the respondents who were not satisfied were also unwilling to recommend the service, how many respondents does this represent?
- How many respondents were either satisfied or willing to recommend the service, but not both?
- If the number of respondents increased to 1,200, how many would be both satisfied and willing to recommend the service?
- 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.
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Math Problem Analysis
Mathematical Concepts
Percentages
Survey Analysis
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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