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?

Short answer

The amount of pure silver to be added is 18 grams.

Step-by-step solution

Step-1. Setup the model.

Total weight of the five rings is$5\times 18=90\text{grams}$

Let is the amount of pure silver to be added.

The given information can be written as:

$10\%\text{silver}+\text{100\%silver}=25\%\text{silver}$

Step-2. Substitute the respective values.

$\begin{array}{l}10\%\times \text{90grams}+\text{100\%}\left(x\right)\text{grams}=25\%\left(90+x\right)\text{grams}\\ \frac{10}{100}\times \text{90grams}+x\text{grams}=\frac{25}{100}\left(90+x\right)\text{grams}\\ 9\text{grams}+x\text{grams}=\frac{1}{4}\left(90+x\right)\text{grams}\end{array}$

Step-3. Simplify the equation.

$\begin{array}{l}9+x=\frac{1}{4}(90+x)\\ 36+4x=90+x\\ 3x=54\\ x=18\end{array}$

Hence, the amount of pure silver to be added is 18 grams.