Final answer:
To obtain a metal that is 35% copper, we use an algebraic equation to find that 75 kilograms of a metal with 25% copper must be mixed with 50 kilograms of a metal with 50% copper.
Step-by-step explanation:
To solve the problem of mixing two different metals to obtain a metal that is 35% copper, we set up an algebraic equation. Let x be the amount in kilograms of the first metal (25% copper) that needs to be mixed.
The total amount of copper from the first metal is 0.25x (since it has 25% copper), and the amount from the second metal (50 kg at 50% copper) is 0.50×50 or 25 kg. For the final mixture to be 35% copper, the total weight of the mixture (x + 50 kg) should have 35% of its weight as copper.
Setting up the equation:
0.25x + 25 = 0.35(x + 50)
Solve for x:
0.25x + 25 = 0.35x + 17.5
0.10x = 7.5
x = 75 kg
Therefore, 75 kilograms of the first metal must be mixed with 50 kilograms of the second metal to obtain a metal that is 35% copper.