A metalworker has a metal alloy that is 25% copper and another alloy that is 60% copper. How many kilograms of each alloy should the metalworker combine to create 60kg of a 46% copper alloy?
Let's represent the amount of the 25% copper alloy as x kg.
Therefore, the amount of copper in the 25% alloy is 0.25x kg.
Similarly, the amount of the 60% copper alloy is 60 - x kg.
Therefore, the amount of copper in the 60% alloy is 0.6(60 - x) kg.
To combine the alloys, the amount of copper in the resulting alloy should be 46% of the total weight which is 0.46(60) kg.
Setting up the equation:
0.25x + 0.6(60 - x) = 0.46(60)
0.25x + 36 - 0.6x = 27.6
-0.35x = -8.4
x = 24
Therefore, the metalworker should combine 24 kg of the 25% copper alloy and 60 - 24 = 36 kg of the 60% copper alloy to create 60 kg of a 46% copper alloy.