Question

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?

Answer 1

Answer: There are 7 students who want French only.

Step-by-step explanation:

Since we have given that

Number of students is planning schedules = 30

Number of students who want to take French = 16

Number of students who want to take Spanish = 16

Number of students want to take Latin = 11

Number of students who take both  French and latin = 5-3 =2

Number of students who take French and Latin and Spanish as well = 3

Number of students who only want Latin = 5

Number of students who only want spanish = 8

According to venn diagram, we get that

$a+b+g+f=16\\\\c+d+e+g=11\\\\b+e+f+g=16$

So, it becomes,

$c+d+e+g=11\\\\5+2+e+3=11\\\\e=11-(5+2+3)=1$

Similarly,

$b+e+f+g=16\\\\8+1+f+3=16\\\\12+e=16\\\\e=16-12\\\\e=4$

Similarly,

$a+d+g+f=16\\\\a+2+3+4=16\\\\a=16-(2+3+4)\\\\a=16-9\\\\a=7$

Hence, there are 7 students who want French only.