cigarettes, 101 drank alcohol regularly and used illegal drugs, 106 smoked cigarettes and a used illegal drugs. 85 engaged in all three behaviors, and 131 engaged in none of these behaviors. 1250 students were surveyed. How many drank alcohol or used illegal drugs?

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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1250 were surveyed, 911 drank alcohol or used illegal drugs, 425 drank alcohol only. How many drank alcohol and used illegal drugs, but did not smoke cigarettes?
### College Student Substance Use Survey

An anonymous survey of college students was conducted to determine behaviors concerning alcohol, cigarettes, and illegal drugs. The key findings from the survey are as follows:

- **836** students reported drinking alcohol regularly.
- **624** students reported smoking cigarettes.
- **176** students reported using illegal drugs.
- **395** students drank alcohol regularly and smoked cigarettes.
- **101** students drank alcohol regularly and used illegal drugs.
- **106** students smoked cigarettes and used illegal drugs.
- **85** students engaged in all three behaviors: drinking alcohol, smoking cigarettes, and using illegal drugs.
- **131** students did not engage in any of these behaviors.

A total of **1,250** students participated in the survey.

**Question:**  
How many students either drank alcohol or used illegal drugs?

**Explanation:**
To find the number of students who drank alcohol or used illegal drugs, you need to identify the overlap between those two groups and avoid double-counting those who engaged in both behaviors.

This survey is useful for understanding substance use trends among college students and can help in designing better educational and health interventions to address these behaviors.
Transcribed Image Text:### College Student Substance Use Survey An anonymous survey of college students was conducted to determine behaviors concerning alcohol, cigarettes, and illegal drugs. The key findings from the survey are as follows: - **836** students reported drinking alcohol regularly. - **624** students reported smoking cigarettes. - **176** students reported using illegal drugs. - **395** students drank alcohol regularly and smoked cigarettes. - **101** students drank alcohol regularly and used illegal drugs. - **106** students smoked cigarettes and used illegal drugs. - **85** students engaged in all three behaviors: drinking alcohol, smoking cigarettes, and using illegal drugs. - **131** students did not engage in any of these behaviors. A total of **1,250** students participated in the survey. **Question:** How many students either drank alcohol or used illegal drugs? **Explanation:** To find the number of students who drank alcohol or used illegal drugs, you need to identify the overlap between those two groups and avoid double-counting those who engaged in both behaviors. This survey is useful for understanding substance use trends among college students and can help in designing better educational and health interventions to address these behaviors.
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