A metalworker has a metal alloy that is 25% copper and another alloy that is 70% copper. % copper. How many kilograms of each alloy should the metalworker combine to create 60 kg of a 52% copper alloy?
Let's assume that x kilograms of the 25% copper alloy is used in the mixture, and y kilograms of the 70% copper alloy is used.
To find the amount of copper in the mixture, we multiply the mass of each alloy by their respective copper percentages and sum them up:
0.25x + 0.70y = 0.52 * 60.
Simplifying the equation:
0.25x + 0.70y = 31.2.
Since we have two variables, we need another equation. The total mass of the alloys is 60 kg, so:
x + y = 60.
We can solve this system of equations using substitution, elimination, or matrix methods. In this case, we'll use the substitution method:
Rearrange the second equation to express y in terms of x:
y = 60 - x.
Substitute the value of y in the first equation:
0.25x + 0.70(60 - x) = 31.2.
Simplifying:
0.25x + 42 - 0.70x = 31.2.
-0.45x = -10.8.
x = 24.
Substituting this value into the second equation:
y = 60 - 24 = 36.
Therefore, the metalworker should combine 24 kg of the 25% copper alloy and 36 kg of the 70% copper alloy to create 60 kg of a 52% copper alloy.