# A nickle is approximately 20 mm in diameter and a quarter is about 25 mm in diameter. If the...

## Question:

A nickle is approximately 20 mm in diameter and a quarter is about 25 mm in diameter. If the nickel enlarges to a diameter of 128 mm, then what would be the diameter of the quarter using the same scale?

## Ratio and Proportion:

The ratio of two values may be maintained by finding their proportion and using it to find the corresponding pair of values with the same ratio as the first.

The ratio of nickle to quarter diameter is 20:25. This may be written as a fraction: {eq}\dfrac{20}{25}{/eq} or {eq}\dfrac{4}{5}{/eq}.

When the nickle is enlarged to 128 mm, let x be the corresponding diameter of the quarter. The ratio of the enlarged coins is 128:x or {eq}\dfrac{128}{x}{/eq}.

The two proportions must be equal to maintain the scale.

\begin{align} \dfrac{4}{5}=&\dfrac{128}{x}\\ 4x=&128\times5&&\left[\text{Cross multiply}\right]\\[0.3cm] 4x=&640\\ x=&160&&\left[\text{Divide both sides by 4}\right]\\[0.3cm] \end{align}

The diameter of the quarter must be 160 mm.