SOLUTION: An automobile dealer has 200 new cars on his lot. 90 cars have automatic transmissions, 60 cars have air conditioning and 40 have both. How many cars DO NOT have either automatic

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: An automobile dealer has 200 new cars on his lot. 90 cars have automatic transmissions, 60 cars have air conditioning and 40 have both. How many cars DO NOT have either automatic      Log On


   

Question 1173156: An automobile dealer has 200 new cars on his lot. 90 cars have automatic
transmissions, 60 cars have air conditioning and 40 have both. How many cars
DO NOT have either automatic transmissions or air conditioning?
Found 2 solutions by ikleyn, Boreal:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

The number of cars that have at least one of the listed features is


    90 + 60 - 40 = 110.    (*)


The rest,  200 - 110 = 90 cars HAVE NO any of the two listed features.    ANSWER


Explanation


    In formula (*), you add the numbers 90 and 60 due to obvious reason.

    You then subtract the number of 40, BECAUSE you count these 40 cars TWICE, when you add 90 and 60.

Solved.

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To see many other similar solved problems,  see the lesson
    - Counting elements in sub-sets of a given finite set
in this site.



Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
40 have both AC and AT
so 50 more have AT alone
and 20 more have AC alone
That is 110 cars
The rest do not have either: There are 90 without either.