How many ounces of pure gold must be added to 10 ounces of a gold alloy that is 30% gold to make an alloy that is 50% gold?
You now have 30% Au in a 10 oz piece which is 3 g Au and 7 g other.
Let x = amount pure Au to be added to the 10 oz piece.
(x + 3)/(x + 10) = 0.50