In an examination, candidates could take any one, any two or all of Latin, French and German.

Out of \(100\) candidates \(4\) took Latin only, \(13\) took French only and \(12\) took German only. There were \(5\) who took all three languages and \(20\) who did not take French.

The average mark in French of all of the candidates who took this subject was \(50\)%. Within this group there were the following average marks in French:

\(\qquad\) Those taking French only, \(57\)%.

\(\qquad\) Those taking French and Latin, \(45\)%.

\(\qquad\) Those taking French and German, \(52\)%.

\(\qquad\) Those taking all three languages, \(35\)%.

Calculate the number who took Latin and German, the number who took French and Latin and the number who took French and German.

There is a lot of information in this question. It might help to draw a Venn diagram with a Latin bubble, a French bubble, and a German bubble so that these overlap.

If we fill in the number of people in each region, can we then write down relationships between the remaining unknown numbers?

If we know the average number of marks received per candidate in French, can we find out how many marks were earned by the candidates in French in total?