a metalworker has a metal alloy that is 20% copper and another alloy that is 70% copper. how many kilograms of each alloy should the metalworker combine to create 100 kg of a 50% copper alloy?

The metalworker should use 60 kg of metal alloy that is 70% copper and 40 kg of metal alloy that is 20% copper.

Step-by-step explanation:

System of Equations

Let's call  

x=amount of metal alloy that is 20% copper

y=amount of metal alloy that is 70% copper

The metalworker wants to create 100 Kg of 50% copper alloy. This gives us the first relation

x+y=100

The combination of 20% of x and 70% of y will produce 50% of the sum of both, thus

20x+70y=50(x+y)

Operating

20x+70y=50x+50y

Reducing and dividing by 10

2y=3x

The system of equations is easily solved by isolating x in the first equation

x=100-y

And replacing into the last equation

2y=3(100-y)

Operating

2y=300-3y

5y=300

y=60

Thus

x=100-60=40

The metalworker should use 60 kg of metal alloy that is 70% copper and 40 kg of metal alloy that is 20% copper.

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step-by-step explanation: