A class has 30 students. 21 students like math and 9 like english . If 16 students like math only and 5 students like neither math nor English, how many students like both math and English? Draw a Venn diagram to represent the information.
Everybody in the red circle likes math.
Everybody in the blue circle likes English.
a = the number who like math only
b = the number who like both math and English.
c = the number who like English only.
d = the number who do not like either math or English.
A class has 30 students. So a+b+c+d = 10
21 students like math. So a+b = 21
9 like English. So b+c = 9
16 students like math only. So a = 16
5 students like neither math nor English. So d = 5
how many students like both math and English?
Since 21 like math of which 16 like math only, the other 5 must like both math
and English. So we have the answer immediately, 5 like both.
Draw a Venn diagram to represent the information.
a=16, b=5 (which is the answer).
We have everything in the Venn diagram except c. But since 9 like English,
and since 5 like both, the other 4 must like English only. So c = 4.
We didn't need to be told that there are 30 students. We could have figured
that out just by adding 16+5+4+5 = 30.
Edwin