In Mike's English class at university there are 178 students, of whom 51 also study history and 44 also study statistics. There are another 85 students who also study history, of whom 25 study statistics also. Another 35 students study only statistics. If 15 students study all three of these subjects, how many in total study statistics?
I get 104. What do you get?
got 98 but im not sure where im missing the extra 15. i know i added the 15 in the center im sure of it
To find out how many students study statistics in total, we can use the principle of inclusion-exclusion.
Let's break down the information given:
- Total number of students in Mike's English class at university: 178
- Number of students who study both English and history: 51
- Number of students who study both English and statistics: 44
- Number of students who study both history and statistics: 15
- Number of students who study only statistics: 35
- Number of students who study both English, history, and statistics: 15
To determine the total number of students who study statistics, we'll add up the number of students who study only statistics and those who study both English and statistics.
1. Number of students who study only statistics: 35
2. Number of students who study both English and statistics: 44
Adding these two numbers together: 35 + 44 = 79
Therefore, in total, 79 students study statistics.
To find the total number of students who study statistics, we need to add together the following numbers:
1. The number of students who study only statistics.
2. The number of students who study statistics and history but not both.
3. The number of students who study statistics and history and statistics.
4. The number of students who study statistics and no other subjects.
Let's break it down step by step:
Step 1: The number of students who study only statistics.
From the given information, we know that 35 students study only statistics.
Step 2: The number of students who study statistics and history but not both.
We can find this number by subtracting the number of students who study both statistics and history (15 students) from the number of students who study history and statistics (44 students) but not including the 15 students who study all three:
44 - 15 = 29 students
Step 3: The number of students who study statistics and history and statistics.
We already know that 15 students study all three subjects.
Step 4: The number of students who study statistics and no other subjects.
To find this number, we need to subtract the number of students who study both history and statistics (25 students) from the number of students who study history and statistics (44 students), excluding the 15 students who study all three:
44 - 25 = 19 students
Now, let's add up all the numbers:
35 + 29 + 15 + 19 = 98
Therefore, there are a total of 98 students who study statistics.