# A model plane is 1/48 the size of the actual plane. If the model plane is 28 inches long, how long is the actual plane?

May 30, 2017

$112 f e e t$

#### Explanation:

The particular wording of the question is stating that the model is the fraction $\frac{1}{48} \text{th}$ of the whole plane. In other words, this is a fraction. Not a ratio. The two are quite different.

Let the actual length of the plane be $x$ in inches.

Then we have:

$\frac{1}{48} \times x = 28$

Multiply both sides by $\textcolor{red}{48}$ - gets the $x$ on its own.

$\textcolor{g r e e n}{\frac{1}{48} \times x \textcolor{red}{\times 48} \text{ "=" } 28 \textcolor{red}{\times 48}}$

$\textcolor{g r e e n}{\frac{\textcolor{red}{48}}{48} \times x \text{ "=" } 28 \textcolor{red}{\times 48}}$

But $\frac{48}{48} = 1 \mathmr{and} 1 \times x = x$

$x = 1344 \text{ inches}$

To change this into feet we need to determine how many lots of 12 inches we can fit into 1344 inches (12 inches = 1 foot).

$\frac{1344}{12} = 112 f e e t$