Question 246070
100 travelers total.


your categories are:


a = number travelers who know english.
b = number of travelers who know russian.
c = number of travelers who do not know english and do not know russian.
d = number of travelers who know both english and russian.


a + b + c - d = 100


a = 75
b = 83
c = 10
d = ?????


75 + 83 + 10 - d = 100
168 - d = 100
d = 68


You have 68 people who know english and russian.


here's how it works


you have 75 people who know english.


this includes 68 people who know english and russian.


you have 83 people who know russian.


this includes 68 people who know english and russian.


the people who know english and russian are being counted twice.   Once in the english group and once in the russian group.


You remove the double counting by subtracting them one time.


75 + 83 + 10 - 68 = 100


Another way to accomplish this would be to create new categories as follows:


f = speak english only
g = speak russian only
h = not speak (english and russian)
i = speak both english and russian


your numbers would be:


7 + 15 + 10 + 68 = 100