Question

[I absolutely don't get this, please help] Sterling silver is an alloy of 92.5% sliver and 7.5% copper by weight. You have 15 ounces of 800 grade silver which is 80% silver and 20% copper. How much pure silver should you add to the 800 grade to make sterling silver?​

Answer 1

If $s$ is the amount of pure silver you add to the alloy, then the new alloy will have a total weight of $15+s$ oz. You want 92.5% of this alloy to be silver, so that the amount of silver in the new alloy is $0.925(15+s)$.

80% of the starting 15 oz alloy was silver; this comes out to 12 oz. To this amount we are adding $s$. So

$0.925(15+s)=12+s$

and solving this tells you that you need to add $s=25$ oz of silver to get the sterling silver alloy.