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 create 90 kg of a 64% copper alloy?
the metalworker should use ___ kilograms of the metal alloy that is 20% copper and ___ kilograms of the metal alloy that is a 75% copper
Let x be the amount (in kilograms) of the metal alloy that is 20% copper.
Then the amount of copper in this alloy is 0.2x.
The amount of the alloy that is 75% copper is 90 - x.
Then the amount of copper in this alloy is 0.75(90 - x).
The total amount of copper in the final alloy is 0.64 * 90 = 57.6 kg.
So the equation to solve is:
0.2x + 0.75(90 - x) = 57.6
0.2x + 67.5 - 0.75x = 57.6
-0.55x + 67.5 = 57.6
-0.55x = 57.6 - 67.5
-0.55x = -9.9
x = -9.9 / -0.55
x = 18
So the metalworker should use 18 kilograms of the metal alloy that is 20% copper and 90 - 18 = 72 kilograms of the metal alloy that is 75% copper. Answer: \boxed{18, 72}.