Question

A jeweler has 5 rings, each weighing 12 g, made of an alloy of 20% silver and 80% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 64%. How much silver should she add?

Answer 1

We have been given that a jeweler has 5 rings, each weighing 12 g, made of an alloy of 20% silver and 80% gold.

Upon melting all 5 rings, the weight of the material will be 12*5=60 grams.

We have been given that the alloy contains 20% silver and 80% gold. Further, let us assume that x grams of silver are added to the melted material so that it has 64% gold and 36% silver.

Therefore, we can set up an equation:

$\text{Amount of gold before mixing}=\text{Amount of gold after mixing}$

Therefore, we get an equation:

$80\%\text{ of 60 gram}=64\%\text{ of (x+60) gram}$

$0.80*60=0.64(x+60)\\48=0.64x+38.4\\0.64x=9.6\\x=\frac{9.6}{0.64} \\x=15$

Therefore, 15 grams of silver must be added to the melted material in order to reduce the gold content to 64%.