Copper that was 95% pure was melted together with copper that was 75% pure to make 15 kilograms of an alloy that was 83% pure. How many kilograms of each kind were used?
Mass of 95% pure copper:
Mass of 75% pure copper:
The first piece of information that you're going to use is the fact that you know how much alloy you have and its purity, which means that you know how much copper it contains.
More precisely, the alloy contains
At the same time, the masses of actual copper must add up to give 12.45 kg. This means that you can write
Use the first equation to write
This means that
So, if you mix 7.8 kg of 95% pure copper with 7.2 kg of 75% pure copper you get a 15 kg of 83% pure copper alloy.