A metalworker has a metal alloy that is 30% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 80kg of a 51% copper alloy?

Step-by-step explanation:

If x is the mass of 30% copper alloy, and y is the mass of 65% copper alloy, then:

x + y = 80

0.30x + 0.65y = 0.51 (80)

Solving the system of equations using substitution:

0.30x + 0.65 (80 - x) = 0.51 (80)

0.30x + 52 - 0.65x = 40.8

11.2 = 0.35x

x = 32

y = 80 - x

y = 48

The metalworker needs 32 kg of 30% copper alloy and 48 kg of 65% copper alloy.