Bunuel wrote:
If Juanita gives half of her bitcoins in a 1: 2 ratio to Pat and Svetlana, respectively, then Pat will have one fourth as many bitcoins as will Svetlana, who will in turn have twice as many bitcoins as will Juanita. If Pat currently has 2 bitcoins, then how many more bitcoins does Juanita currently have than Svetlana?
A. 8
B. 12
C. 20
D. 22
E. 24
Solution:
We can let 6x = the number of bitcoins Juanita currently has. So if she gives x bitcoins to Pat and 2x bitcoins to Svetlana (notice that x + 2x = 3x is half of 6x), then Pat will have 2 + x bitcoins and Svetlana will have 4(2 + x) = 8 + 4x bitcoins (notice that Pat having ¼ as many bitcoins as Svetlana means Svetlana having 4 times as many bitcoins as Pat). Since Svetlana will in turn have twice as many bitcoins as will Juanita, we can create the equation:
8 + 4x = 2(3x)
8 + 4x = 6x
8 = 2x
4 = x
Therefore, Juantia currently has 6x = 6(4) = 24 bitcoins.Svetlana will have 8 + 4(4) = 24 bitcoins if Juanita gives her 2(4) = 8 bitcoins. Therefore, Svetlana currently has 24 - 8 = 16 bitcoins and thus Juanita has 24 - 16 = 8 more bitcoins than Svetlana.
Answer: A
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