word translation:- please explain each step especially last

[Anusha.h]

In a used car lot, there are 3 times as many red cars as green cars. If tomorrow 12 green cars are sold and 3 red cars are added, then there will be 6 times as many red cars as green cars. How many green cars are currently in the lot?

[Brent@GMATPrepNow]

In a used car lot, there are 3 times as many red cars as green cars. If tomorrow 12 green cars are sold and 3 red cars are added, then there will be 6 times as many red cars as green cars. How many green cars are currently in the lot?

Let's solve the question using 1 variable.

Let G = current # of green cars
There are 3 times as many red cars as green cars.
So, 3G = current # of red cars

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NOW WE'll EXAMINE THE INFORMATION FOR TOMORROW
If tomorrow 12 green cars are sold and 3 red cars are added . . .
# of green cars tomorrow = G - 12
# of red cars tomorrow = 3G + 3

. . . then there will be 6 times as many red cars as green cars.
At the moment, we have (G - 12) green cars and (3G + 3) red cars.
These two values aren't equal, because we're told that there are 6 times as many red cars as green cars.
How do we make the 2 values equal so that we can get an equation to work with?
Just multiply the number of green cars by 6.
So, we get 6(G - 12) = 3G + 3
Expand: 6G - 72 = 3G + 3
Rearrange: 3G = 75
Solve: G = 25

Since G = current # of green cars, there are currently 25 green cars.

Cheers,
Brent

[GMATGuruNY]

in a used car lot, there are 3 times as many red cars as green cars. if tomorrow 12 green cars are sold and 3 red cars are added, then there will be 6 times as many red cars as green cars. how many green cars are currently in the lot?

10
15
20
25
30

I've added answer choices, which the GMAT would provide.
We can plug in the answers for the current number of green cars.

Answer choice C: g=20
Since there are 3 times as many red cars as green cars, r = 3*20 = 60.
AFter 12 green cars are sold, new g = 20-12 = 8.
After 3 red cars are added, new r = 60+3 = 63.
(new red)/(new green) = 63/8 ≈ 8.
Since the resulting number of red cars must be only SIX times the resulting number of green cars, the current number of green cars must INCREASE.
Eliminate A, B and C.

Answer choice D: g=25
Since there are 3 times as many red cars as green cars, r = 3*25 = 75.
AFter 12 green cars are sold, new g = 25-12 = 13.
After 3 red cars are added, new r = 75+3 = 78.
(new red)/(new green) = 78/13 = 6.
Success!

The correct answer is D.

[Anusha.h]

Thanks a lott Brent, GMATGuru.