In an interview of 50 math majors,
12 liked calculus and geometry
18 liked calculus but not algebra
4 liked calculus, algebra and geometry
25 liked calculus
15 liked geometry
10 liked algebra but neither calculus nor geometry
2 liked geometry and algebra but not calculus.
Of those surveyed, how many liked calculus and algebra?
If you want the number that liked both calculus and algebra, there is only one category that fits that description.
I hope this helps.
To find out how many math majors liked calculus and algebra, we need to analyze the given information.
We know that:
- 12 liked calculus and geometry
- 18 liked calculus but not algebra
- 4 liked calculus, algebra, and geometry
- 25 liked calculus
- 15 liked geometry
- 10 liked algebra but neither calculus nor geometry
- 2 liked geometry and algebra but not calculus
To calculate the number of math majors who liked calculus and algebra, we can use the principle of inclusion-exclusion.
First, let's start with the total number of people who liked algebra, which includes those who liked both algebra and calculus and those who liked algebra but not calculus. From the given information, we know that 10 liked algebra but neither calculus nor geometry, and we also know that 2 liked algebra and geometry but not calculus. So, the total number of people who liked algebra is 10 + 2 = 12.
Now, let's subtract those who liked calculus but not algebra from the total number of people who liked calculus. We know that 18 liked calculus but not algebra, so the number of people who liked both calculus and algebra is 25 - 18 = 7.
Therefore, 7 math majors liked calculus and algebra.