SOLUTION: Hello, this question is not about matrices, but I could not find a category that corresponded with my question! A Chevrolet dealer has 160 new cars for sale on her lot. Among th

Question 487330: Hello, this question is not about matrices, but I could not find a category that corresponded with my question!
A Chevrolet dealer has 160 new cars for sale on her lot. Among these cars, 50 have four-cylinder engines, 80 have a tilted steering wheel, 30 have power windows, 42 have four-cylinder engines and a tilted steering wheel, 18 have four-cylinder engines and power windows, 15 have all three features, and 65 have none of the features. How many of these cars have a tilted steering wheel and power windows? How many cars have at least one of these features? How many cars have exactly 2 of these features?
Thanks so much.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
You need to draw a Venn diagram to solve this.
It's hard to explain without showing you a
drawing, but it looks like 3 interlocking
circles with all 3 circles overlapping in the center.
If you google "Venn diagram" you will see.
The inside of each circle represents the number
of cars in the 3 main categories, 4 cyl, pw, and tsw
4 cyl = 50
pw = 30
tsw = 80
---------
Where the circles overlap, try to see the regions as:
(1) 4 cyl and pw, but not tsw
(2) 4 cyl and tsw, but not pw
(3) pw and tsw, but not 4 cyl
(4) all 3 features in the center
Try to find the number of cars that fall into
each of these 4 regions
----------
First, there are 160 cars, but 65 don't fall into the 3 categories,
so there are 95 cars total
42 have four-cylinder engines and a tilted steering wheel
This is how many fall in the overlap between 4 cyl and tsw
Subtract and you have the region
(2) 4 cyl and tsw, but not pw
-----------
18 have four-cylinder engines and power windows
Subtract . Now you have the region
(1) 4 cyl and pw, but not tsw
-----------
Look at the region which is pw and nothing else. Call it
If I add up all the tsw, which is and ,
and , I should get

This is pw and nothing else
Now subtract This is the region
(3) pw and tsw, but not 4 cyl
-------------
Now you can find
Only 4 cyl =
Only tsw =
Only pw =
--------------
Knowing all these regions, you can answer any question, like
How many of these cars have a tilted steering wheel and power windows?

How many cars have at least one of these features?
have at least one
How many cars have exactly 2 of these features?

---------
Note that is you add up all the 7 regions, you should get

OK
Hope this helps- at least you're on the right track now
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