A silversmith combined pure silver that cost $30.48 per ounce with 52 oz of a silver alloy that cost $21.35 per ounce. How many ounces of pure silver were used to make an alloy of silver costing $24.76 per ounce?

oz

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