Answer:
- English: 57
- Ilocano: 28
- Both: 15
Explanation:
Given a group of 100 persons, of which 72 speak English and 43 speak Ilocano, you want to know the numbers who speak one language only, and the number who speak both languages.
Both
It usually works well to work Venn diagram problems by first considering the number in the region where all groups overlap. In this case, that is the group that speaks both languages.
Adding the counts of English speakers and Ilocano speakers, we find that the number of persons who speak both are counted twice. That is, the total will exceed the total number of persons by the number who speak both languages.
72 +43 = 115
115 -100 = 15 . . . . number who speak both languages
English
We know that 15 of the English-speakers speak both languages, so the number who speak English only will be ...
72 -15 = 57 . . . . number who speak only English
Ilocano
Likewise, 15 of the Ilocano-speakers speak both languages, so the number who speak Ilocano only will be ...
43 -15 = 28 . . . . number who speak Ilocano only
__
In the attached diagram, you will notice the total of the numbers in the English circle is 72, and the total in the Ilocano circle is 43. The total of all numbers in the diagram is 100, the number of persons in the group.