40 students study arabic 16 students ancient greek 43 students study latin

Question

from a survey of 100 students 70 indicated that they were studying at least one of the three langauges 

 

11 students study both arabic and accent greek 13 students study both arabic and latin 6 students study both arabic and ancient greek how many students study none of these languages? how many students study all three of the languages? how many study only ancient greek

Answer 1

Using a Venn diagram, see:

 

https://www.wyzant.com/resources/files/396074/abc_venn_diagram/download?encryptedID=VX6s8lTyNig%3D&d=v

 

take the the numbers given to you in the question and figure out how many of the 100 students are in each of the eight disjoint pieces (note when you are done the eight numbers you put in the diagram must add up 100 and still satisfy the conditions given in the problem. Then  you will be able to figure out the answer to each part of your problem.

 

Let A=Arabic, B=Greek, C=Latin and go from there.

 

 

Any questions comment back.