Question

The town library surveyed visitors to determine their reading references. Fifty people said they like mysteries, 30 said they like history, and 6 said they like science fiction. However, of these, 5 like mysteries and history, 3 like history and science fiction, 2 like mysteries and science fiction, and 1 likes all three. Find the number of visitors surveyed.

Answer 1

In the Venn diagram above the labelled regions have the following meanings:

A=0 because all the visitors use the library.

B: mystery readers only

C: history readers only 

D: science fiction (SF) readers only

E: mystery and SF but not history

F: history and SF but not mystery

G: mystery and history but not SF

H: all three

B+E+G+H=50 (mystery)

C+F+G+H=30 (history)

D+E+F+H=6 (SF)

E=2 (mystery+SF)

F=3 (history+SF)

G=5 (mystery+history)

H=1

Now we can substitute values for the letters.

B=50-(E+G+H)=50-8=42.

C=30-(F+G+H)=30-9=21.

D=6-(E+F+H)=6-6=0.

Total = A+B+C+D+E+F+G+H=0+42+21+0+2+3+5+1=74.

74 visitors were surveyed.