The red circle represents the set of households with VCRs.
The blue circle represents the set of households with VCRs.
1. "a" is the number of households with VCRs only, the left
part of the red circle.
2. The overlapping part of both circles represents the set of
households with both VCRs and DVDs.
"b" is the number of households with both VCRs and DVD's.
3. "c" is the number of households with DVDs only, the right
part of the blue circle.
4. "d" represents the number of households which have neither
a VCR nor a DVD.
The question is:
How many households only own one or more DVD players?
So we want to know what "c" equals.
In a survey of 380 households regarding the ownership of VCRs and DVD players, the following data was obtained:
350 households own one or more VCRs.
180 households own one or more VCRs and one or more DVD players.
13 households do not own a VCR or a DVD player.
Those three sentences translate into these equations
respectively:
a+b+c+d = 380
a+b = 350
d = 13
Subtract the second equation from the first:
c+d = 30
Substitute d = 13 into that:
c+13 = 30
c = 17
{This problem is obviously from a very old book.
One dated back when DVDs had just come on the
market. Nobody has VCRs anymore unless they're
left over from way back then. :) ]
Edwin
