Thread: Venn Diagrams

I have a question with 3 parts, I have done the first 2 parts but i cannot make sense of the last part and was wondering if someone could please help me?

Q: 75 pupils, 48 pupils like ready salted, 35 like cheese & onion

i) if 7 pupils do not like either flavor, how many like both?
A: 15

ii) *what is the greatest possible number of pupils who could like both?
A: 35

**what is the smallest possible number of pupils who could like both?
A: 8

Now this is the part that i cannot figure out:

The number of pupils who like both is twice the number who do not like either;

iii) what fraction of the pupils who like ready salted do not like cheese & onion?

Hello, wahhdoe!

75 pupils: 48 pupils like ready salted, 35 like cheese & onion.

i) If 7 pupils do not like either flavor, how many like both?
. . . Answer: 15

iia) What is the greatest possible number of pupils who could like both?
. . . Answer: 35

iib) What is the smallest possible number of pupils who could like both?
. . . Answer: 8

All correct . . . Good work!


Now this is the part that i cannot figure out:

The number of pupils who like both is twice the number who do not like either;

iii) What fraction of the pupils who like ready salted do not like cheese & onion?

I often use a chart instead of a Venn diagram . . .


. .



We are told: .

. .



Reading across, we can fill in the empty cells:

. .



Reading down, we have two equations:

. .



The chart becomes:

. .


Now you can answer the question.