How many people drink tea in the morning? How many people drink coffee in the morning? How many people drink only tea in the morning? How many people drink only coffee in the morni... How many people drink tea in the morning? How many people drink coffee in the morning? How many people drink only tea in the morning? How many people drink only coffee in the morning? How many people drink both coffee and tea? How many people drink coffee or tea? How many people do not drink coffee or tea? How many people took the survey?
Understand the Problem
The question is asking for information regarding a survey represented in a Venn diagram about people's beverage preferences in the morning, specifically focusing on tea and coffee. Each part of the question seeks specific counts related to those who drink tea, coffee, or both.
Answer
- a. 52, b. 55, c. 27, d. 30, e. 25, f. 55, g. 27, h. 82
Answer for screen readers
- a. 52 people drink tea in the morning.
- b. 55 people drink coffee in the morning.
- c. 27 people drink only tea in the morning.
- d. 30 people drink only coffee in the morning.
- e. 25 people drink both coffee and tea.
- f. 55 people drink coffee or tea (this includes both).
- g. 27 people do not drink coffee or tea (assumed from total).
- h. 82 people took the survey.
Steps to Solve
- Identify Total Drinkers of Tea and Coffee
From the Venn diagram, we can gather that:
- People who drink only tea = 27
- People who drink only coffee = 30
- People who drink both tea and coffee = 25
- Calculate Total for Each Beverage
To find out how many people drink tea and coffee:
-
Total drinking tea = Only tea + Both [ \text{Total Tea} = 27 + 25 = 52 ]
-
Total drinking coffee = Only coffee + Both [ \text{Total Coffee} = 30 + 25 = 55 ]
- Determine Only Tea and Only Coffee Drinkers
- People who drink only tea = 27
- People who drink only coffee = 30
- Find the Total Number of People Drinking Both Beverages
People who drink both coffee and tea = 25 (this is given directly from the diagram).
- Calculate Total Survey Participants
Total people who took the survey can be calculated by summing up all unique groups: [ \text{Total} = (\text{Only Tea}) + (\text{Only Coffee}) + (\text{Both}) = 27 + 30 + 25 = 82 ]
- a. 52 people drink tea in the morning.
- b. 55 people drink coffee in the morning.
- c. 27 people drink only tea in the morning.
- d. 30 people drink only coffee in the morning.
- e. 25 people drink both coffee and tea.
- f. 55 people drink coffee or tea (this includes both).
- g. 27 people do not drink coffee or tea (assumed from total).
- h. 82 people took the survey.
More Information
Venn diagrams are an excellent tool for visually representing overlapping sets, helping to clarify how many participants fall into each category based on shared attributes—in this case, the beverage preferences in the morning.
Tips
- Miscounting Overlaps: Failing to distinguish between those who drink only one beverage and those who drink both can lead to confusion.
- Total Calculation Error: Forgetting to sum all unique groups correctly can result in undercounting the survey participants.
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