SOLUTION: A survey asked 1000 college students which courses they were taking this semester. The survey obtained the following information: - 347 are taking a Math course - 343 are taki

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Question 1198452: A survey asked 1000 college students which courses they were taking this semester. The survey obtained the following information:
- 347 are taking a Math course
- 343 are taking a English course
- 39 are taking both a Science and a English course
- 8 are taking a Math course, a Science course, and a English course
- 65 are taking both a Math and a English course
- 758 are taking a Science course or a English course
- 221 are taking a Math course but not a Science course nor a English course
a.) use the information listed to complete a three-circle venn diagram M,E,and S.
b.) using the results from the venn diagram in question a.), determine how many students:
i.) are taking a science course:
ii.) are taking an English course but not a Math course:
iii.) are not taking a Math course
iv.) are taking at least two of the types of courses (Math, English and Science):
Found 3 solutions by math_tutor2020, greenestamps, MathTherapy:
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

Just realized I made a mistake, so ignore my previous post.
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


I found the response from the other tutor hard to follow; and it appears his final Venn diagram does not satisfy the given data....

We are given the following information:
(A) 347 are taking a Math course
(B) 343 are taking a English course
(C) 39 are taking both a Science and a English course
(D) 8 are taking a Math course, a Science course, and a English course
(E) 65 are taking both a Math and a English course
(F) 758 are taking a Science course or a English course
(G) 221 are taking a Math course but not a Science course nor a English course

I'll let you draw the Venn diagram and fill in the numbers in the different regions, using the following sequence of calculations.

(1) Use (D) to show 8 students taking all three courses
(2) Use (C) to show 31 students taking Science and English but not Math
(3) Use (E) to show 57 students taking Math and English but not Science
(4) Use (G) to show 221 students taking only Math
(5) Use (B) to show 247 students taking only English
(6) Use (A) to show 61 students taking Math and Science but not English
(7) Use (F) to show 354 students taking Science only

You now have the numbers for all regions in the Venn diagram, so you can answer the questions that are asked.
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
A survey asked 1000 college students which courses they were taking this semester. The survey obtained the following information:
- 347 are taking a Math course
- 343 are taking a English course
- 39 are taking both a Science and a English course
- 8 are taking a Math course, a Science course, and a English course
- 65 are taking both a Math and a English course
- 758 are taking a Science course or a English course
- 221 are taking a Math course but not a Science course nor a English course
a.) use the information listed to complete a three-circle venn diagram M,E,and S.
b.) using the results from the venn diagram in question a.), determine how many students:
i.) are taking a science course:
ii.) are taking an English course but not a Math course:
iii.) are not taking a Math course
iv.) are taking at least two of the types of courses (Math, English and Science)
As requested, numbers that are taking math, science, and english are M, S, and E, respectively
We find that number that take:	math only, is: M, only
				science only, is: S, only
				english only, is: E, only
					
				math and science, only, is: M&S
				math and english, only, is: M&E

				science and english, only, is: S&E
				math, science, and english, is: M&S&E
					
The VENN DIAGRAM below has been labeled as such.
.

M   = M, only + M&E + M&S&E + M&S
347 = 221 + 57 + 8 + M&S ------ Substituting 347 for M, 221 for M, only, 57 for M&E, and 8 for M&S&E
347 = 286 + M&S
347 - 286 = M&S
61 = M&S

E = 343, so E, only += 343 - (31 + 8 + 57) = 343 - 96 = 247

S or E = S, only + S&E + E, only + M&S&E + M&S + M&E
   758 = S, only + 31  +   247   +   8   +  61 + 57 
   758 = S, only + 404
758 - 404 = S, only
      354 = S, only

We now get the following VENN DIAGRAM with all variables’ values entered
  .
I’ll start you off with: How many i.) are taking a science course:
                                               S = S, only + S&E + M&S&E + M&S 
S, or number of students taking a science course =   354   + 31  +   8   +  61 = 454
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