8. A goldsmith has 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold. How

much pure gold must be added to this alloy to obtain an alloy that is 90% pure gold?

The amount of pure gold that should be added is

(Type an integer or a decimal.)

grams.

Answer: 65 grams

Step-by-step explanation:

If 130 grams of a gold alloy (a mixture of gold and one or more other metals) containing 85% pure gold, that means the percentage of other metals will be;

100 - 85 = 15 %

You should first calculate the amount of gold that makes up this percentage.

That is, 85% of 130 grams.

85/100 * 130 = 110.5

Then, let X be what will be added to the above value to make 90%. So,

(110.5 + X) / (130 + X) * 100 = 90

Divide both sides by 100

(110.5 + X) / (130 + X) = 90/100

(110.5 + X) / (130 + X) = 0.9

Cross multiply and open the bracket

110.5 + X = 117 + 0.9X

Collect the like terms

X - 0.9X = 117 - 110.5

0.1X = 6.5

Divide both sides by 0.1

X = 6.5/0.1

X = 65 grams

Therefore, the amount of pure gold that should be added is 65 grams