Question

In a group of 60 students, 31 speak French, 23 speak Spanish and 14 speak neither French nor Spanish. Determine the number of students who speak: french only

Answer 1

Answer: 23

Work Shown

60 total students

14 speak neither French nor Spanish

60-14 = 46 speak either French, or Spanish, or both.

F = set of people who speak French

S = set of people who speak Spanish

Use the inclusion-exclusion principle to solve the equation below.

n(F union S) = n(F) + n(S) - n(F intersect S)

46 = 31 + 23 - x

That equation solves to x = 8, which means n(F intersect S) = 8 and furthermore it means there are 8 people who speak both languages.

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There are 31 students who speak French and 8 who speak both.

31-8 = 23 students speak French only.

Refer to the Venn diagram shown below.