A metalworker has a metal alloy that is 20% copper and another alloy that is 65% copper. How many kilograms of each alloy should the metalworker combine to create 100 kg of a 56% copper alloy?
The metalworker should use _kilograms of the metal alloy that is 20% copper and _kilograms of the metal alloy that is 65% copper.
(Type whole numbers.)

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carlosego carlosego · Answer 1 · 2019-02-02T21:59:30+01:00

Answer:

The metallurgist must use 20 kilograms of the metal alloy which is 20% copper and 80 kilograms of the metal alloy which is 65% copper.

Step-by-step explanation:

We call the alloy 20% copper.

We call the alloy 65% copper.

Let's call the new version you want to create.

When mixing the M Alloy with the S you want to obtain 100 kg of the new alloy

[tex]M + S = 100[/tex] (i)

Then

[tex]0.2M + 0.65S = 100(0.56)[/tex] (ii)

We substitute (i) in (ii)

[tex]0.2(100-S) + 0.65S = 100(0.56)[/tex]

[tex]20 - 0.2S + 0.65S = 56[/tex]

[tex]0.45S = 36[/tex]

[tex]S = \frac{36}{0.45}[/tex]

[tex]S = 80 kg[/tex] (iii)

Now we substitute (iii) in (i)

[tex]M + 80 = 100[/tex]

[tex]M = 20[/tex]