Final answer:
By using the given numbers and setting up equations, we can determine that 5 people like tea but not coffee in a group of 20 people.
Step-by-step explanation:
To find out how many people like tea but not coffee in a group of 20, we must consider the given information:
- 13 people like tea.
- 12 people like coffee.
- 3 people like neither tea nor coffee.
First, we need to calculate the total number of people who like either tea or coffee or both. Since 3 people like neither, this means 20 - 3 = 17 people like either tea or coffee or both. Now let's let T be the number of people who like tea but not coffee, C be those who like coffee but not tea, and B be those who like both tea and coffee.
We can set up the equations based on the information given:
- T + B = 13 (the number of people who like tea)
- C + B = 12 (the number of people who like coffee)
- T + C + B = 17 (the number of people who like either or both)
By solving these equations, we can find the value of T, the number of people who like tea but not coffee. We know that T + C + 2B = 13 + 12, which simplifies to T + C + 2B = 25. Since 17 people like either or both, B must be equal to 25 - 17 = 8. This means 8 people like both tea and coffee.
Subtracting the number of people who like both from the total number of tea lovers, we find that T = 13 - 8, which means that 5 people like tea but not coffee.