a metalworker has a metal alloy that is 15 % copper and another alloy that is 60 % copper. how many kilograms of each alloy should the metalworker combine to create 100kg of a 51 % copper alloy?

Let x = kg of 15% copper alloy

Let y = kg of 60% copper alloy

Since we need to create 60 kg of alloy we know:

x + y = 60

42% of 60 kg = 25.2 kg of copper

So we're interested in creating 25.2 kg of copper

We need some amount of 15% copper and some amount of 60% copper to create 25.2 kg of copper:

0.15x + 0.60y = 25.2

but

x + y = 60

x = 60 - y

substituting that value in for x

0.15 (60 - y) + 0.60y = 25.2

9 - 0.15y + 0.60y = 25.2

0.45y = 16.2

y = 36

Substituting this y value to solve for x gives:

x + 36 = 60

x = 24

Therefore, in order to create 60 kg of a 42% alloy, we'd need 24 kg of 15% copper and 36 kg of 60% copper.