A metalworker has a metal alloy that is 20% copper and another alloy that is 75% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 53% copper alloy?
The metalworker should use __ kilograms of the metal alloy that is 20% copper and __ kilograms of the metal alloy that is 75% copper
Let x be the number of kilograms of the metal alloy that is 20% copper.
Then, the number of kilograms of the metal alloy that is 75% copper is 90 - x.
The amount of copper in the metal alloy that is 20% copper is 0.2x kg.
The amount of copper in the metal alloy that is 75% copper is 0.75(90 - x) kg.
The total amount of copper in the final alloy is 0.53(90) kg.
Since the total amount of copper in the final alloy is the sum of the amount of copper in the two alloys, we have the equation:
0.2x + 0.75(90 - x) = 0.53(90)
0.2x + 67.5 - 0.75x = 47.7
-0.55x = -19.8
x = (-19.8)/(-0.55)
x ≈ 36
Therefore, the metalworker should use 36 kilograms of the metal alloy that is 20% copper and 90 - 36 = 54 kilograms of the metal alloy that is 75% copper. Answer: \boxed{36, 54}.