Edwin'solution:
First draw a big rectangle to hold all 150 people surveyed:
Next draw a circle to hold all 75 people who liked
cherry and label it C (for "cherry"):
Next draw a circle overlapping the first circle to
hold all 94 people who liked orange and label
it O.
The overlapping part will contain the 22 people who
liked both, so we write "22" in the region that's shaped
like this " () ", the overlapping region of the two
circles.
Now since 75 people liked cherry, and 22 of those 75 are
accounted for because they also liked orange. the rest
of them, the other 75-22 or 53, are over in the left side of
circle C. So we write 53 in the left part of circle C.
Now since 94 people liked orange, and 22 of those 94 are
accounted for because they also liked cherry. the rest
of them, the other 94-22 or 72, are over in the right side of
circle O. So we write 72 in the right part of circle O.
Now we have placed 53+22+72 or 147 of the 150 people. So
that leaves only 150-147 or 3 people who didn't like cherry
or orange. They go in the rectangle outside both circles.
I'll put those 3 people down on the bottom left side of the
rectangle outside both circles:
a) How many liked only orange flavor?
The 72 which are in the part of circle O which does
not overlap circle C.
b) How many liked only cherry flavor?
The 53 which are in the part of circle C which does
not overlap circle O.
c) How many liked either one or the other or both?
There are two ways to figure that:
Either add up the ones that are in either circle
or both circles: 53+22+72=147
or the easy way, subtract the 3 that did not like either
flavor from the 150 and get 150-3 = 147. Either way, the
answer is the same.
d) How many liked neither?
That's just the 3 that are outside both circles.
Edwin
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