Question

The number 48 needs to be divided into two parts, so that one part is three times larger than the other. What are those parts?

Answer 1

`12+36=48`

Explanation:

Just for the hell of it lets go against what other people would do and avoid using the letter `x` for the unknown value. The point I am making is that we are free to use what we like as long as we declare it.
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Let the first part be represented by `f` (for first)
Let the second part be represented by `s`

It is given that the second part is 3 times larger than the other. So we write: `color(red)(s=3color(green)(f))`

We are told that `color(green)(f+color(red)(s)=48)`

However we also know that `color(red)(s=3color(green)(f))` so we can substitute.

`color(green)(f+color(red)(s)=48 color(white)("dddd") -> color(white)("dddd") f+color(red)(3)f=48)`

`color(green)(color(white)("ddddddddddd.d") ->color(white)("dddddd") 4fcolor(white)(".d") =48)`

Divide both sides by 4

`4/4f=48/4`

`color(white)(".d") f=12`

So we have `12+36=48`