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4 November, 05:23

A metalworker has a metal alloy that is 20 % copper and another alloy that is 60 % copper. How many kilograms of each alloy should the metalworker combine to create 80 kg of a 52 % copper alloy?

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  1. 4 November, 06:00
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    16 kg of I type and 64 kg of II type should be mixed.

    Step-by-step explanation:

    Given that a metal alloy in original has 20% copper and 80% other metals.

    Another mixture contains 60% copper and 40% other metals.

    We have to get a new alloy of 80 kg which has 52% copper.

    Let us assume that we mix x kg of I alloy and y kg of second alloy.

    Then we have x+y = total weight = 80 kg.

    x+y = 80 ... (i)

    Next condition is that new alloy has 52% copper in it

    When we mix x kg of I, and y kg of II, copper content would be

    0.2x+0.6y. This equals 52% of 80 = 41.6

    Or Dividing by 0.2 we get

    x+3y = 208 ... (ii)

    (ii) - (i) gives 2y = 128 or y = 64 kg

    x = 16 kg

    16 kg of I type and 64 kg of II type should be mixed.

    Verify:

    Copper in new alloy = 16 (0.2) + 64 (0.6) = 3.2+38.4 = 41.6

    = 52% of 80
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