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?

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.

He should add 1.68 grams of silver

Explanation:

Mass of alloy = 14 grams

% of silver = 15%

% of gold = 100 - 15 = 85%

If he decides to reduce the gold to 73%, the percentage of silver will become (100 - 73 = 27%)

Mass of 15% silver = 0.15*14 grams = 2.1 grams

Mass of 27% silver = 0.27*14 grams = 3.78 grams

Amount of silver to add = 3.78 - 2.1 = 1.68 grams