Question

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?

Answer 1

`112 feet`

Explanation:

The particular wording of the question is stating that the model is the fraction `1/48"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:

`1/48xx x=28`

Multiply both sides by `color(red)(48)` - gets the `x` on its own.

`color(green)(1/48 xx xcolor(red)(xx48)" "=" "28color(red)(xx48))`

`color(green)((color(red)(48))/48 xx x" "=" "28color(red)(xx48))`

But `48/48=1 and 1xx x=x`

`x=1344" 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).

`1344/12=112 feet`