A jar is filled with red, white, and blue tokens that are

swerve wrote:A jar is filled with red, white, and blue tokens that are equivalent except for their color. The chance of randomly selecting a red token, replacing it, then randomly selecting a white token is the same as the chance of randomly selecting a blue token. If the number of tokens of every color is a multiple of 3, what is the smallest possible total number of tokens in the jar?

A. 9
B. 12
C. 15
D. 18
E. 21

The OA is D

Source: Manhattan Prep

We can let r, w, and b be the number of red, white, and blue tokens in the jar. Thus we have:

r/(r + w + b) x w/(r + w + b) = b/(r + w + b)

rw/(r + w + b)^2 = b/(r + w + b)

rw/(r + w + b) = b

rw = br + bw + b^2

Since r, w, and b are multiples of 3, we can let b = r = 3. So we have:

3w = 9 + 3w + 9

However, this equation yields no solution. Now let’s let b = 3 and r = 6; we have:

6w = 18 + 3w + 9

3w = 27

w = 9

So the minimum number of tokens in the jar is 3 + 6 + 9 = 18.

Answer: D