# 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

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 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(9681)   (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