Suppose we draw a huge red circle P and a huge blue circle F like the above on
an athletic ball field, and require each of the 50 students to stand in the red
circle if the attend piano lessons, to stand in the blue circle if they attend
flute lessons, to stand in both circles if they attend both, but not to stand
in the red circle if they don't attend piano lessons, and not to stand in the
blue circle if they don't attend flute lessons.
We let a = the number who attend piano but not flute.
We let b = the number who attend both piano and flute.
We let c = the number who attend flute but not piano.
We let d = the number who do not attend piano or flute.
A school offers piano lessons and flute lessons to a group of 50 children.
Therefore a+b+c+d=50
28 attend piano lessons
Therefore a+b = 28
17 attend flute lessons
Therefore b+c = 17
12 attend neither piano lessons nor flute lessons.
Therefore d=12.
We have the system:
Substituting 12 for d
gives:
Subtracting the second equation from the first gives c=10
Subtracting the third equation from the first gives a=21
Substituting a=21 in a+b=28 gives b=7
So we have:
find the number of children who attend only the
piano lessons.
That's a = 21, the number standing in the red circle P but not in the
blue circle F.
Edwin
