A metalworker has a metal alloy that is 25 % copper and another alloy that is 55 % copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 43 % copper alloy?

To determine the answer, we need to set up equations. We do this by doing mass balances. We let

x = A alloy 25% copper

y = B alloy 55% copper

Overall Mass balance:

x + y = 100

Copper mass balance:

.25x +.55y =.43 (100) = 43

SOlving simultaneously, we get:

x = 99.67 kg 25% copper alloy

y = 0.33 kg 55% copper alloy