The formulas are right.
10K electroplated Au means there is just a thin layer of 10K gold on the surface; the remainder of the jewelry is something else. 10K means 10/24 = 5/12 Au and 14/24 = 7/12 something else.
You're right that 24K Au is pure Au.
18K Au is 18/24 = 9/12 Au and 6/24 = 3/12 something else.
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