SOLUTION: in a group og 15 persons ,7 persons have studied German,8have studied French and 3 persons have not studied either.How many persons of these have studied both German and French?

Algebra ->  Equations -> SOLUTION: in a group og 15 persons ,7 persons have studied German,8have studied French and 3 persons have not studied either.How many persons of these have studied both German and French?       Log On


   

Question 875842: in a group og 15 persons ,7 persons have studied German,8have studied French and 3 persons have not studied either.How many persons of these have studied both German and French?
Found 2 solutions by ewatrrr, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
Answer by Theo(13342) About Me  (Show Source):
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7 have studied german
8 have studied french
3 have studied neither.
total of persons is 15.

make a table: 

                                 german       french       neither     total

                                    7            8            3          18

the total should be 15 but the total is 18.
this means 3 people have been double counted.
they couldn't have come out of the neither category, so they must have come from the german and french category.
the german category includes people who have studied both german and french.
the french category includes people who have studied botyh german and french.
those people have been double counted.
they must be equal to 3.
let's revise the table to see what happens:
out new categories are:
german DISABLED_event_only= 7 - 3 = 4
french DISABLED_event_only= 8 - 3 = 5
german and french DISABLED_event_only= 3
neither = 3
now when we add them up together we get a total of 15 as we should.

the new table looks like this:
        german only     french only    german and french    neither     total

              4              5                3                 3          15


now we're good and the answer is:

3 people have studied german and french