A metalworker has a metal alloy that is 15% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to crea of a 47% copper alloy?
Let's say the metalworker wants to combine x kilograms of the 15% copper alloy and y kilograms of the 55% copper alloy.
The amount of copper in the 15% alloy is: 0.15x
The amount of copper in the 55% alloy is: 0.55y
To create a 47% copper alloy, the total amount of copper in both alloys should be 0.47 times the total weight of the new alloy (x + y).
So we have the equation:
0.15x + 0.55y = 0.47(x + y)
Now, let's solve this equation for x and y:
0.15x + 0.55y = 0.47x + 0.47y
0.15x - 0.47x = 0.47y - 0.55y
-0.32x = -0.08y
x = (-0.08y)/(-0.32)
x = 0.25y
We can substitute this value of x in the equation to find y:
0.15(0.25y) + 0.55y = 0.47(0.25y + y)
0.0375y + 0.55y = 0.47(1.25y)
0.5875y = 0.5875y
y = 1
Now that we have y = 1, we can find x:
x = 0.25y = 0.25(1) = 0.25
Therefore, the metalworker should combine 0.25 kilograms of the 15% copper alloy and 1 kilogram of the 55% copper alloy to create 1.25 kilograms of a 47% copper alloy.