A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper. How many kilograms of each alloy should the metalworker combine to create 50 kg of a 50% copper alloy?
The metalworker should use __ kilograms of the metal alloy that is 55% copper. kilograms of the metal alloy that is 30% copper and ___kilograms of the
metal alloy that is 55% copper.
Let x represent the number of kilograms of the metal alloy that is 55% copper.
Therefore, 50-x represents the number of kilograms of the metal alloy that is 30% copper.
To calculate the total amount of copper in the final alloy, we need to find the sum of the copper content in each alloy.
For the metal alloy that is 55% copper:
Copper content = 0.55x
For the metal alloy that is 30% copper:
Copper content = 0.30(50-x) = 15 - 0.30x
Since we want to create a 50 kg alloy that is 50% copper, the copper content in the final alloy would be:
0.50(50) = 25
Now, we can set up the equation:
0.55x + 15 - 0.30x = 25
Simplifying the equation:
0.25x = 10
x = 40
The metalworker should use 40 kilograms of the metal alloy that is 55% copper.
Therefore, 50-40 = 10 kilograms of the metal alloy that is 30% copper.