How many people like atleast two types of chocolate?

Question

Two hundred people have come to hear a lecture on the benefits of chocolate. A survey is given out at the beginning as to the chocolate preferences of the audience members. Suppose 120 people like dark chocolate, 100 people like milk chocolate, 60 people like white chocolate, 40 people do not like any kind of chocolate and 10 people like all three kinds of chocolate, how many people like at least two types of chocolate?

Answer 1

200 people total but 40 people do like any chocolate, therefore, include only total who like chocolate
TC = 200 - 40 = 160 people voted for some type of chocolate listed

 

Now assume:

 

A = number of people who only voted for one type of chocolate (either dark, milk, or white)

B = number of people who only voted for two types of chocolate

C = number of people who voted for all three types = 10

D = number of people who like at least two types of chocolate = B + C

 

dark chocolate votes = 120

milk chocolate votes = 100

white chocolate votes = 60

 

Therefore, total chocolate votes = A + 2*B + 3*C  = 120 + 100 + 60 = 280

C= 10

 

A + 2*B + 3*(10) = 280

A  + 2*B  = 250

 

and  A + B + C = 160 people voting for 1, 2, and 3 types of chocolate

A + B + 10 = 160

A + B = 150

 

Therefore, two eqns, two unknowns:

1)     A + 2*B  = 250

2) - [A  + B  =  150]

------------------------

0 + B = 100

A = 150 - B  = 150 - 100 = 50

C = 10

D = B + C = 100 + 10 = 110 people like at least two types of chocolate