Q:

is planning schedules for 30 students Sixteen students say they want to take French, 16 want to take Spanish, and 11 want to take Latin Five say they want to take both French and Latin, and of these, 3 wanted to take Spanish as well. Five want only Latin, and 8 want only Spanish Draw a Venn diagram describing this situation How many students want French only?

Accepted Solution

A:
Answer: There are 7 students who want French only.Step-by-step explanation:Since we have given that Number of students is planning schedules = 30Number of students who want to take French = 16Number of students who want to take Spanish = 16Number of students want to take Latin = 11Number of students who take both Β French and latin = 5-3 =2Number of students who take French and Latin and Spanish as well = 3Number of students who only want Latin = 5Number of students who only want spanish = 8According to venn diagram, we get that [tex]a+b+g+f=16\\\\c+d+e+g=11\\\\b+e+f+g=16[/tex]So, it becomes,[tex]c+d+e+g=11\\\\5+2+e+3=11\\\\e=11-(5+2+3)=1[/tex]Similarly,[tex]b+e+f+g=16\\\\8+1+f+3=16\\\\12+e=16\\\\e=16-12\\\\e=4[/tex]Similarly,[tex]a+d+g+f=16\\\\a+2+3+4=16\\\\a=16-(2+3+4)\\\\a=16-9\\\\a=7[/tex]Hence, there are 7 students who want French only.