Need help solving a Venn Diagram I am trying to figure out how to solve this Venn diagram problem for my Discrete Mathematics class. So the problem goes like this:
In a school there are 420 students. 300 of them have gone to school by car, 80 of them walking, 120 on a bicycle, 46 in a car and walking, 26 in a car and a bicycle, 36 walking and a bicycle, but 22 of them have neither used a car, bicycle or walked.
a) How many students come to school by car, walking and cycling? b) How many students come on a bicycle and walking but not car?
I just can't find a way to find the missing x in the middle I need to find
 A: The three cricles represent $398 (=420-22)$ students. This area is equal to the sum of the partial areas of the three circles. First add the whole three cirlces. $398=300+80+120...$. Now you have counted the intersections of two events twice. Thus you have to substract them.  $398=300+80+120-46-36-26...$.
The intersection of all 3 circles has been first counted three times. After substracting the intersections of 2 circles the intersection is not counted anymore. Thus you have to add it.
$398=300+80+120-46-36-26+x$

A: Well, I got something like that. The b section is pretty easy from there. Hope I didn't mess up.

Some calculations.

A: I approached this from two extremes to start with:
First I assumed the missing x is 0.  This leads to the number of people only walking being -2 and the total people being 414.   This is clearly wrong!
Then I assumed the maximum x, which will be 26.  This leads to a total of 440 people.  This is also clearly wrong, but the answer is somewhere between!
However - I then realised that the difference between 440 and 414 is 26 - which is also the difference between the missing x of 0 and the second of 26.   Logically therefore, and correctly, if you put x as 6 it works.
