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31 March, 18:40

A karat equals 1/24 part of gold in an alloy [ eg 9 karat gold is 9/24 gold]. How many grams of 9 karat gold must be mixed with

18 karat gold to make 200 grams of 14 karat gold alloy?

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  1. 31 March, 22:07
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    This is a mixture problem.

    Let the 9 karat gold to be mixed be x. The 18 karat would weight (200 - x). Since the total = 200g.

    mass1 * karat1 + mass2*karat = total mass * total carat

    Let mass1 be x g. mass 2 would be = (200 - x)

    karat 1 = 9 karat 2 = 18

    Total mass = 200g.

    Total karat = 14.

    9*x + 18 * (200 - x) = 14*200

    9x + 18*200 - 18*x = 14*200

    18*200 + 9x - 18x = 14*200

    3600 - 9x = 2800

    3600 - 2800 = 9x

    800 = 9x

    9x = 800

    x = 800/9

    x ≈ 88.89

    Therefore 88.89 grams of 9 karat gold must be mixed.
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