A jeweler has five rings, each weighing g, made of an alloy of silver and gold. She decides to melt down the rings and add enough silver to reduce the gold content to . How much silver should she add

Complete question :

A jeweler has five rings, each weighing 18 g, made of an alloy of 10% silver and 90% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 75%. How much silver should she add?

Kindly check explanation

Explanation:

Given the following :

Weight of each alloy = 18g

Initial % of Silver = 10% = 0.1

Initial % of Gold = 90% = 0.9

New % of gold = 75% = 0.75

Hence, new % of silver will be (1 - 0.75) = 0.25

Let the amount of silver to be added = s

Hence,

Initial gold content = final gold content + added silver

18 * 0.9 = 0.75(18 + s)

16.2 = 13.5 + 0.75s

16. 2 = 13.5 + 0.75s

16.2 - 13.5 = 0.75s

2.7 = 0.75s

s = 2.7 / 0.75

s = 3.6

S = 3.6

Hence the amount of silver needed per ring in other to reduce the gold content = 3.6g

Total for the 5 rings = (3.6 * 5) = 18g