Question

a metalworker has meal alloy that is 15% copper and another alloy that is 60% copper. how many kilograms of each alloy should the metalworker combine to create 100 kg of a 42% copper

Answer 1

Let L be the low copper alloy and H be the high copper alloy.
We need 0.15L + 0.60H = 0.42 and L + H = 100

L=100 - H
Substituting this into the second equation for L, we get:
0.15(100-H) + 0.60H = 0.42(H+L)
15 - 0.15H + 0.60H = 0.42(H+100-H)
15 + 0.45H = 0.42(100)
0.45H = 42 - 15 = 27
H = 27/.45 = 60 lbs

Back substitution, L = 40 lbs.