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Venn Diagram Problem

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Junior | Next Rank: 30 Posts
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Venn Diagram Problem

by mattocks » Sun Mar 28, 2010 11:30 am
All coffee mixtures sold in a store contain Colombian, Jamaican or Brazilian coffee or some combination of these. Of all mixtures, 33 contain Colombian coffee, 43 contain Jamaican coffee and 42 contain Brazilian coffee. Of these, 16 contain at least Colombian and Jamaican coffee. 18 contain at least Jamaican and Brazilian coffees, 8 contain at least Brazilian and Colombian coffees and 5 contain all three. How many different coffee mixtures are there?

a) 45
b) 56
c) 76
d) 81
e) 86
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by thephoenix » Sun Mar 28, 2010 7:53 pm
mattocks wrote:All coffee mixtures sold in a store contain Colombian, Jamaican or Brazilian coffee or some combination of these. Of all mixtures, 33 contain Colombian coffee, 43 contain Jamaican coffee and 42 contain Brazilian coffee. Of these, 16 contain at least Colombian and Jamaican coffee. 18 contain at least Jamaican and Brazilian coffees, 8 contain at least Brazilian and Colombian coffees and 5 contain all three. How many different coffee mixtures are there?

a) 45
b) 56
c) 76
d) 81
e) 86
Colombian-------->=a+b+d+e =33
Jamaican -------->=b+c+e+f=43
Brazilian -------->=d+e+f+g=42
16 contain at least Colombian and Jamaican coffee.
-------->=b+e=16
18 contain at least Jamaican and Brazilian coffees, -------->=e+f=18
8 contain at least Brazilian and Colombian coffees-------->=d+e=8
and 5 contain all three. -------->=e=5
so b=11
f=13
and d=3
therefore a=14
c=14
and g=21

How many different coffee mixtures -------->a+b+d+ec+f+g=81
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by eaakbari » Mon Mar 29, 2010 12:42 pm
Yep D is good
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