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Question 126499: Please show me how to solve this problem ( it was a homework problem (1 complete problem) and I didn't know where to start). thanks!
200 Students
70 Students take English class
54 Students take Math class
45 Students take Social Studies
28 Students take English and Math
19 Students take English and Scial Studies
15 Students take Math and Scial Studies
10 Students take English, Math and Social Studies
1.) How many students take English
2.) How many Students take math only
3.) How many Students take English, social studies but not math
4.) How many students take math and social studies but not English class
5.) How many do not take any class.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! See diagram below:
The rectangle represents all 200 students.
The green circle represents those students that take English
The blue circle represents those students that take Math
The red circle represents those students that take Social Studies
The area where the circles intersect represents those students that take two or three of the classes.
We know that 10 students take all three classes mentioned, so we put a 10 into the space in the center that is the intersection of all three circles.
We know that 15 students take Math and Social Studies, but we have already accounted for 10 of these students because these 15 include the 10 who take all three classes. So in the intersection of the M and S circles, we put 15 - 10 = 5.
Similarly, there are 28 students taking English and Math, but 10 are already accounted for, so 18 (28 - 10) goes into the intersection of the M and E circles. The intersection of the E and S circles gets a 9 (19 - 10).
Now that we have all of the intersection spaces filled, we can enter numbers in the non-intersected parts of the circles. 45 students take SS, but we have accounted for 10 + 9 + 5 = 24 of them already, so 21 remain who must only be taking Social Studies -- 21 goes in the S circle. Likewise, 21 goes in the M circle, and 33 goes in the Math circle.
Now you can start answering the questions:
1. How many students take English? You are given this answer, 70.
2. How many students take Math only? Look at the diagram. What is the number of students that are in the M circle, but in no other circle?
3. How many students take English and Social Studies but not Math? What is the number in the intersection of the E and S circles excluding that part that is also part of the M circle?
4. How many take Math and Social Studies but not English. What is the number in the intersection of the M and S circles excluding that part that is also part of the E circle?
5. How many do not take any class? I presume that implies 'any class of the three listed' There are a total of 200 students. Add up all of the numbers in the circles and their intersections and subtract from 200.
I'm going to let you do the counting and the addition.
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