A metalworker has a metal alloy that is 25% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 60kg of a 57% copper alloy?
Let x be the amount of the 25% copper alloy and y be the amount of the 65% copper alloy.
We know that x + y = 60kg.
We also know that the amount of copper in x is 0.25x and the amount of copper in y is 0.65y.
The total amount of copper in the final alloy is 0.57 * 60 = 34.2kg.
So, 0.25x + 0.65y = 34.2.
Let's solve the system of equations:
x + y = 60
0.25x + 0.65y = 34.2
We can solve the first equation for x:
x = 60 - y
Substituting this into the second equation, we get:
0.25(60 - y) + 0.65y = 34.2
15 - 0.25y + 0.65y = 34.2
0.4y = 19.2
y = 19.2 / 0.4
y = 48
Substituting y back into the first equation, we get:
x + 48 = 60
x = 60 - 48
x = 12
So, the metalworker needs to combine 12kg of the 25% copper alloy and 48kg of the 65% copper alloy to create 60kg of a 57% copper alloy.