Problem Solving

Source of Q: MGMAT test 3:
Sally has a gold credit card with a certain spending limit, and a platinum card with twice the spending limit of the gold card. Currently, she has a balance on her gold card that is 1/3 of the spending limit on that card, and she has a balance on her platinum card that is 1/5 of the spending limit on that card. If Sally transfers the entire balance on her gold card to her platinum card, what portion of her limit on the platinum card will remain unspent?
1) 11/30
2) 29/60
3) 17/30
4) 19/30
5) 11/15

My Solution is giving me an ans of 19/15 - Please help fix the gap in my solution:


Let the Spending limit on the Gold Card be X
Thus: Spending limit on the Platinum Card = 2X

Balance on the Gold Card = x/3
Balance on the Platinum Card = 2x/5

After Sally Transfer's the balance from the gold card to the platinum card:
New Balance on the platinum card = x/3 + 2x/5 = 11x/15

Thus: Unspend amount left on platinum card =
2x - 11x/15 = 19x/15


Advice is greatly appreciated.
Regards.

Thus: Unspend amount left on platinum card =
2x - 11x/15 = 19x/15

19x/15 is the unspent portion of a total of 2x.

Therefore 19x/15/2x = 19/30 is the answer

Thank you...that explains the missing step.