venn diagrams

Question

In a recent sixth grade survey, out of 324 students, the following information was collected regarding condiments for hot dogs. The results were: 144 liked mustard, 241 liked ketchup, 97 liked pickle relish, 49 liked ketchup and pickle relish but not mustard, 14 liked mustard and pickle relish but not ketchup, 81 like mustard and ketchup but not pickle relish, and 32 like only mustard. 

 

How many do not like any of these three condiments on their hot dog?

 

How many like exactly one of these three on their hot dog? 

 

how many like exactly two of these three on their hot dog? 

Answer 1

Mustard =A

Ketchup=B

Pickle relish=C

 

A=144

B=241

C=97

 

A and B but not C =81

 

B and C but not A =49

 

A and C but not B =14

 

Only A =32

 

With this data once we draw the Venn diagram, we find that

 

A and B and C =  144 - (14+81)-32=17

 

B and not A and not C =241-(81+17+49)=94

 

C and not A and not B = 97-(14+17+49)=17

 

How many liked exactly two of the

Three hotdogs

=14+81+49=144

 

How many liked exactly one of these three hotdogs=32+94+17=143