# How to build the equation for this question?

In a class, there are $20$ people. In this class, there are $4$ people who know only english, $9$ who don't know french, $7$ who don't know english. Then, how many people who know both language are there?

Here is my venn diagram

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$$r(1) = \text {who know english}$$ $$r(3) = \text {who know french}$$ $$r(2) = \text {who know both}$$ $$r(4) = \text {who know no language}$$

I'm building the equation now

$$\sum_{i = 1} r(i) = 20$$ $$r(1) + r(2) + r(3) + r(4) = 20$$ $$r(1) = 4$$

I don't have any idea about how to find $r(2)$. What is the correct equation we ought to use?

• Let E be the number who speak English. F be the number who speak French. Then 20 - E = 4, 20 - F = 9. The r notation is too clumbsy to work with. – William Elliot Nov 5 '17 at 19:51

The fact that there are $9$ people who don't know French means that there are $9$ people outside the $F$ circle, meaning that:

$$r(1)+r(4)=9$$

Likewise, the fact that there are $7$ people who don't know English means that there are $9$ people outside the $E$ circle, meaning that:

$$r(3)+r(4)=7$$

I assume you can take it from there.

$r(1)+r(4)=9;\;r(3)+r(4)=7$

$r(1) + r(2) + r(3) + r(4) = 20$

$r(1)=4$

$r(4)=5$

$r(3)=2$

$r(2)=9$