Let x be the amount (in oz) of pure silver used in this alloy. Each ounce of the pure silver contributes a value of $30.48, so that the total cost of the amount of pure silver that gets used is $30.48x.
The same goes for the secondary alloy, where each ounce costs $21.35, so that 52 ounces of the alloy contributes a total cost of $21.35*52.
The final alloy has a total mass of (x + 52) ounces, and each ounce costs $24.76, so that this alloy's totat cost is $24.76*(x + 52).
So we have
30.48x + 21.35*52 = 24.76*(x + 52)
30.48x + 1110.20 = 24.76x + 1287.52
5.72x = 177.32
=> x = 31
