PROBLEM 1-8-3

For every 75 cars made at a factory, 1/3 are red, 20 are blue, and the rest are green.  Seven out of every 10 blue cars have CD players and 40% of the red cars have CD players.  No green cars are produced with CD players.  If the factory produced 960 cars with CD players, how many green cars did it produce?

SOLUTION 1-8-3

If 1/3 of the 75 cars made are red, then 1/3 x 75 = 25.  So, there are 25 red cars, and 20 blue cars.  We are told the rest of the cars are green.  Therefore, 25 + 20 = 45 and 75 – 45 = 30.  So, 30 cars are green.

Blue = 20

Green = 30

Red = 25

Now, 7 out of every 10 blue cars has a CD player.  There are 20 blue cars out of the 75, so that means 14 of them will have CD players (7/10 = ?/20).

Also, 40% of the red cars have CD players, so out of the 75, 25 of them were red.  Therefore, 0.40 x 25 = 10.

Blue (with CD) = 14

Blue (without)  = 20-14 = 6

Red (with CD) = 10

Red (without) = 25-10 = 15

Green (without) = 30

The factory produced 960 cars with CD players.  Our ratio when compared to the 75 cars produced is that the cars with CD players is 24 (14 blue + 10 red).  So, using equivalent fractions,

24/75 = 960/x

So, 75x960/24 = 3000 cars in total produced.

If out of the 75 cars produced, 30 were green, then

30/75 = x/3000

3000x30/75 = 1200

So, there are 1200 green cars.