https://vle.mathswatch.co.uk/images/questions/question1007.png

https://vle.mathswatch.co.uk/images/questions/question1006.png

Guest Apr 29, 2020

#1**+2 **

I like these kinds of questions

So, there's 7 where B, C, and P intersect (the middle).

If there's 12 people in B and C, and 7 of those are already in the BCP, then there's 12 - 7 = 5 people in B and C ONLY (The middle-top intersection), not P

If there's 15 people in B and P, and 7 of those are already in the BCP, then there's 15 - 7 = 8 people in B and P ONLY (The middle-left intersection), not C

If there's 20 people in C and P, and 7 of those are already in the BCP, then there's 20 - 7 = 13 people in C and P ONLY (The middle-right intersection), not C

If there's 35 people in the entire circle of B, and (7 + 5 + 8) = 20 are already in other regions too, then there's 35 - 20 = 15 people in B ONLY (The left huge area)

If there's 32 people in the entire circle of P, and (7 + 8 + 13) = 28 are already in other regions too, then there's 32 - 28 = only 4 people in P ONLY (The bottom huge area)

Now, for the remainder of C, we just add up the values we've already put in the venn diagram, and subtract that sum from the total number of students (60).

That sum is 7 + 5 + 8 + 13 + 15 + 4 = 52

60 - 52 = 8

Therefore, there are 8 people in C ONLY (The right huge area).

Hope you followed along :D

EDIT - forgot to do the other problem :( will make another answer

CentsLord Apr 29, 2020

#3**+1 **

So, problem 2 (forgot to do this one)

The box represents everyone (80 people total).

The people ONLY in the box and NOT in any of the circles are people who don't study French or Spanish. Inferior souls (Just Kidding :D)

And there are 80 - 71 = 9 of those people.

14 people study ONLY Spanish (not answer to c), and **25 people study ONLY** French (is the answer to b)

In the middle (the intersection), there are 71 - (14 + 25) = 71 - 39 = **32 people who study both French and Spanish**.

Now, we know there are 32 + 25 = **57 people studying Spanish** (not only spanish).

:D

CentsLord Apr 29, 2020