Sets question

Question

 A survey was made of the courses taken by 80 students in the fifth year of a school. The figures obtained are shown below: Mathematics only 15; physics and mathematics 40; mathematics but not computer science 35; mathematics 70; Computer science and physics 24; physics 50. How many students took computer science? How many took computer science and physics but not mathematics , draw a Venn diagram to represent your information

Answer 1

The problem is challenging with the Venn Diagram. You MUST draw one!

There is some algebra along the way.

 

Let X be the number of students taking all 3 of math,physics, and computer science.

 

Math only 15;

 

Math but not computer science 35 ---> math and physics = 20

 

Physics and Math = 40 --->  x+20 = 40 ---> x = 20, so X=20 taking all 3 of math, physics, and Computer Science

 

Math = 70 ---> Math and computer science but not physics = 15

 

COmputer Science and Physics (or possibly math)= 24 --->  4 taking computer science and physics only

 

physics (and possibly math and computer science) = 50 ---> physics only 6 

 

since there are 80 students and the total of all the statistics acquired thus far is 80,

there are zero students taking only computer science. That is NO students are taking computer 

science. Computer Science is ALWAYS taken along with another course.

 

The answer to the questions are :

    for computer science = 20 + 15 +4  = 39

 

 Computer Science and Physics but not math = 4 +6 = 10.