Question

The purity of gold is measured in​ karats, with pure gold being 24 karats. other purities of gold are expressed as proportional parts of pure gold. thus​ 18-karat gold is startfraction 18 over 24 endfraction 18 24​, or​ 75% pure​ gold; 12-karat gold is startfraction 12 over 24 endfraction 12 24​, or​ 50% pure​ gold; and so on. how much 2020​-karat gold should be mixed with pure gold to obtain 8080 grams of 2222​-karat ​gold? how much 2020​-karat gold should be​ used?

Answer 1

Answer:

40.2g of the 20 karat gold must be mixed with pure gold to obtain the 22 karat gold

Explanation:

The purity of a 22 karats gold is:

22/24 * 100 = 91.6% of purity

From a gold that is:

20/24 * 100 = 83.3% of purity

We can write:

80g = X + Y (1)

Where X is the mass of the 20-karat gold and Y the mass of pure gold

And in therms of purity:

91.6*80 = 83.3X + 100Y (2)

Replacing (1) in (2):

7328 = 83.3X + 100(80-X)

7328 = 83.3X -100X + 8000

-672 = -16.7X

X =

40.2g of the 20 karat gold must be mixed with pure gold to obtain the 22 karat gold