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7 March, 13:59

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?

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  1. 7 March, 15:15
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    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.
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