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The difference between 10 and 12 is 2, and the difference between 12 and 15 is 3. Write these two numbers as a ratio 2:3.
Then swap them around, that's 3:2, to give you the relative quantities of the two metal-mixtures.
So for the first mixture, 1 kg contains 10% = 100 g of silver. So take 3 kg of this, which will contain 300 g of silver.
The second mixture is 15% silver; so for every 1 kg of this, there will be 150 g of silver. Take 2 kg of this, and you'll also have 300 g of silver.
So, when we add these two quantities together we get 5 kq altogether containing 300 + 300 = 600 g of silver. This is the required 12%.
To get 10 kg altogether, we obviously double the quantities and take 6 kg of the first, and 4 kg of the second.
(It will work with any other number - provided it's between 10% and 15% of course. If you want 11% of silver, the ratio is 1:4 this time. Swap them around and take 4 kg of the first (that will contain 400 g of silver) for every 1 kg of the second (that's 150 g of silver). Total 550 g in 5 kg = 11%. Works every time!)