A metalworker has a metal alloy that is 20% copper and another alloy that is 75% copper. How many kilograms of each alloy should the metalworker combine to create 90 kg of a 53% copper alloy?
The metalworker should use copper and kilograms of the metal alloy that is 20% kilogramsof the metal alloy that is 758opper.
Let x be the number of kilograms of the 20% copper alloy.
Then 90 - x is the number of kilograms of the 75% copper alloy.
The amount of copper from the 20% copper alloy is 0.20*x kg.
The amount of copper from the 75% copper alloy is 0.75*(90-x) kg.
The total amount of copper in the final alloy is 0.53*90 kg.
So, we have the equation:
0.20*x + 0.75*(90-x) = 0.53*90
Simplifying the equation, we get:
0.20x + 0.75*90 - 0.75x = 0.53*90
0.55x + 67.5 - 0.75x = 47.7
-0.20x = -19.8
x = -19.8/-0.20
x = 99
So, the metalworker should use 99 kg of the 20% copper alloy and 90 - 99 = 9 kg of the 75% copper alloy.