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?
the metalworker should use ___ kilograms of the metal alloy that is 15% copper and ___ kilograms of the metal alloy that is 55% copper
Let's assume the metalworker needs to combine a total of x kilograms of the 15% copper alloy and y kilograms of the 55% copper alloy.
The amount of copper in the 15% copper alloy is 0.15x kilograms.
The amount of copper in the 55% copper alloy is 0.55y kilograms.
To create a 47% copper alloy, the total amount of copper in the final alloy should be 0.47(x + y) kilograms.
Therefore, we can set up the equation: 0.15x + 0.55y = 0.47(x + y).
Expanding this equation gives: 0.15x + 0.55y = 0.47x + 0.47y.
Rearranging the terms: 0.47x - 0.15x = 0.55y - 0.47y.
Simplifying: 0.32x = 0.08y.
Dividing both sides by 0.08: x = 0.25y.
Since the metalworker needs to combine a total of x + y kilograms, we can substitute the value of x in terms of y to get: 0.25y + y = x + y.
Simplifying: 1.25y = x + y.
For simplicity, let's assume the total amount of alloy needed (x + y) is 100 kilograms.
Thus, we have the equation: 1.25y = 100.
Dividing both sides by 1.25 gives: y = 80 kilograms.
Substituting this value of y into x = 0.25y, we get: x = 0.25 * 80 = 20 kilograms.
Therefore, the metalworker should use 20 kilograms of the metal alloy that is 15% copper and 80 kilograms of the metal alloy that is 55% copper to create a 47% copper alloy.