how much pure gold ( decigram) should...

Problema Solution

how much pure gold ( decigram) should be added to a 12 karat gold weighing 2 grams in order to achieve 60% gold mixture?

Carat purity is measured as 24 times the pure mass divided by the total mass:

$K = 24\,\frac{M_\text{g}}{M_\text{m}}$

In our case K = 12 k, Mm = 2 gr, we need to find Mg.

12 = 24(Mg/2)

........

........

Mg = 1 g

Mg = 10 dg

Mm = 20 dg

Let 'x' represent the pure gold that we need to add in decigrams

1.00*(x + Mg) + 0(Mm - Mg) = 0.60(Mm + x)

1.00*(x + 10) + 0 = 0.60(20 + 2)

........

........

x = 3.2 dg

3.2 decigrams pure gold should be added to achieve 60% gold mixture.

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