Answer:
There are 87 students signed up for Humanities course only
Explanation:
* Lets explain how to solve the problem
- Its easy to solve this problem using Venn-diagram
- We start with drawing a rectangle and three intersected circles
inscribed in the rectangle
- The rectangle represents all the students courses
- Circle labeled M for mathematics course
- Circle labeled L for Language Arts course
- Circle labeled H for Humanities course
- There are 74 students had signed up for a Math course
- 51 students had signed up for a Language Arts course
- 20 students had signed up for both a Math and Language Arts course
- 10 students had signed up for both a Math and Humanities course
- 5 students had signed up for both a Language Arts and Humanities
course
- 3 students had signed up for all three courses
- 20 students did not sign up for any of these classes
- x students had signed up for Humanities course only
* Lets put these numbers in the venn-diagram
∵ There are 20 students did not sign up for any of these classes
∴ Put 20 inside the rectangle but outside the circles
∵ There are 3 students had signed up for all three courses
∴ Put 3 in the common region between the three circles
∵ There are 5 students had signed up for both a Language Arts and
Humanities course
- 3 student of them are already put in the common part of the 3 circles
∴ Put 5 - 3 = 2 in the common part between circles L and H only
∵ There are 10 students had signed up for both a Math and
Humanities course
- 3 student of them are already put in the common part of the 3 circles
∴ There are 10 - 3 = 7 in the common part between circles M and
H only
∵ There are 20 students had signed up for both a Math and
Language Arts course
- 3 student of them are already put in the common part of the 3 circles
∴ Put 20 - 3 = 17 in the common par between the circles M and L only
∵ 51 students had signed up for a Language Arts course
- We already put 3 + 17 + 2 = 22
∴ Put 51 - 22 = 29 in the empty part of circle L not intersected
with any other circle
∵ There are 74 students had signed up for a Math course
- We already put 3 + 17 + 7 = 27
∴ Put 74 - 27 = 47 in the empty part of circle M not intersected
with any other circle
∵ There are x students had signed up for Humanities course only
∴ Put x in the empty part of circle H not intersected with any other
circle
* Now lets add all the numbers inside the diagram (Bold number)
and then equate them by the total number of the students
∵ The sum of the students in the venn-diagram is:
20 + 3 + 2 + 7 + 17 + 29 + 47 + x = 125 + x
∵ There are 212 SPC students was taken at registration
∴ 125 + x = 212
- Subtract 125 from both sides
∴ x = 87
∵ x represents the students had signed up for Humanities
course only
∴ There are 87 students signed up for Humanities course only
* Look to the attached file for more understand