SOLUTION: Of 100 travelers, 10 understand neither English nor Russian. 75 know English, and 83 know Russian. How many travelers know both English and Russian?

Question 246070: Of 100 travelers, 10 understand neither English nor Russian. 75 know English, and 83 know Russian. How many travelers know both English and Russian?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

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