Question

Joe has a ring weighing 14 grams made of an alloy of 15 % silver and the rest gold. He decides to melt down the rings and add enough silver to reduce the gold content to 73 % . How many grams of silver should he add?

Answer 1

Answer:

2.3 grams.

Explanation:

In the original ring there is 0.15*14 = 2.1 g of silver and 11.9 g of gold.

As there is now 73% of gold in the new ring its total weight is  11.9 / 0.73

= 16.3 g.

Therefore the weight of silver  is now 16.3-11.9 = 4.4 g and the weight of silver added is 4.4 - 2.1  = 2.3 g.

Answer 2

The mass of silver added to the ring is only 1.68 g.

An alloy is defined as a mixture of two or more metals. In this case, the alloy is a mixture of silver and gold. We are told that the mass of the ring is 14 grams. Then it is composed of 15% silver.

Hence;

Amount of silver = 15/100 × 14g = 2.1 g

Amount of gold = (100 - 15)/100 × 14g = 11.9 g

When the amount of amount of gold reduces to  73 %, mass of silver in the ring = (100 - 73)/100 × 14g =3.78 g

Mass of silver added = 3.78 g - 2.1 g = 1.68 g

The mass of silver added to the ring is only 1.68 g.

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