Problema Solution
Every red car at an auto show was a sports car. Half of all blue cars were sports cars. Half of all sport cars were red. There were forty blue cars and thirty red cars. How many cars were neither red nor blue?
Answer provided by our tutors
let
s = the number of all sports cars
b = 40 blue cars
r = 30 red cars
every red car is sports car that this means there are 30 sports and red cars
half of all sports cars were red => s/2 = r that is s/2 = 30 => s = 60 sports cars
s = 60 the number of all sports cars
half of all blue cars are sports cars that is b/2 = 40/2 = 20 are blue and sports cars.
we will find the number of cars that are neither red nor blue by subtracting the number of all cars that are red or blue from the total number of cars
the total number of cars is: sports cars + half of the blue that are not sports
(60 + 40/2) - (30 + 40) = 80 - 70 = 10
10 of the cars are neither red nor blue.
To get understand the solution draw Venn diagram with 3 sets: the set of sports cars, the set of red cars and the set of blue cars.