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13 March, 03:52

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 90 kg of a 51 % copper alloy?

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  1. 13 March, 04:10
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    18 kg of 15% copper and 72 kg of 60% copper should be combined by the metalworker to create 90 kg of 51% copper alloy.

    Step-by-step explanation:

    Let x = kg of 15% copper alloy

    Let y = kg of 60% copper alloy

    Since we need to create 90 kg of alloy we know:

    x + y = 90

    51% of 90 kg = 45.9 kg of copper

    So we're interested in creating 45.9 kg of copper

    We need some amount of 15% copper and some amount of 60% copper to create 45.9 kg of copper:

    0.15x + 0.60y = 45.9

    but

    x + y = 90

    x = 90 - y

    substituting that value in for x

    0.15 (90 - y) + 0.60y = 45.9

    13.5 - 0.15y + 0.60y = 45.9

    0.45y = 32.4

    y = 72

    Substituting this y value to solve for x gives:

    x + y = 90

    x = 90-72

    x=18

    Therefore, in order to create 90kg of 51% alloy, we'd need 18 kg of 15% copper and 72 kg of 60% copper.
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