# If a 14 karat gold necklace weighs 1.8 ounces, how many ounces of pure gold does it contain?

## Question:

If a 14 karat gold necklace weighs 1.8 ounces, how many ounces of pure gold does it contain?

## Application of Ratio and Proportion

An equation with a ratio on both sides is called proportion. If one of the ratios has a missing term taking the cross product can help us solve for the missing term. Ratio and proportion can be used in linearly proportional problems.

Given:

• Karat of gold {eq}14\ \rm karat{/eq}
• Mass of gold {eq}1.8\ \rm ounces{/eq}

The mass of 1 ounce of 14 karat of gold is 0.58 ounces. We can use ratio and proportion to solve for the mass of 1.8 ounces of gold.

\begin{align} 1\ \rm ounce : 0.58\ \rm ounce = 1.8\ \rm ounce : x \end{align}

Solving for x

\begin{align} x(1\ \rm ounce) &= (0.58\ \rm ounce)(1.8\ \rm ounce)\\ x &= \dfrac{(0.58\ \rm ounce)(1.8\ \rm ounce)}{1\ \rm ounce}\\ x &= 1.044\ \rm ounce \end{align}

Therefore the mass of the gold is {eq}1.044\ \rm ounce{/eq}