A metalworker has a metal alloy that is 25% copper and another alloy that is 70% copper. How many kilograms of each alloy should the metalworker combine to create 50 kg of a 52% copper alloy?
The metalworker should use (Type whole numbers.) kilograms of the metal alloy that is 25% copper and kilograms of the metal alloy that is 70% copper.
Let x be the kilograms of the 25% copper alloy.
Then the kilograms of the 70% copper alloy is 50 - x.
The total amount of copper in the 25% alloy is 0.25x kg.
The total amount of copper in the 70% alloy is 0.70(50 - x) kg.
The total amount of copper in the 52% alloy is 0.52(50) kg.
Since the total amount of copper in the 52% alloy is the sum of the copper in the other alloys, we have 0.25x + 0.70(50 - x) = 0.52(50).
0.25x + 35 - 0.70x = 26
Simplifying the equation, we get -0.45x = -9
Dividing both sides of the equation by -0.45, we get x = 20.
Therefore, the metalworker should use 20 kg of the 25% copper alloy and 50 - 20 = 30 kg of the 70% copper alloy. Answer: \boxed{20}.