Question

30 is 15% of what number?

Answer 1

`200`

Explanation:

Let `x` be the number:

Then,

`rarr15/100(x)=30`

`rarr3/20(x)=30`

`rarr(3x)/20=30`

`rarr3x=20*30`

`rarr3x=600`

`rarrx=600/3=200`

Answer 2

A lot of detail given in the explanation so that you can see where everything comes from.

30 is 15% of 200

Explanation:

`color(blue)("Preamble")`

You can think of % as a sort of unit of measurement but one that is worth `1/100`

So `15%" "->" "15xx%" "->" "15xx1/100=15/100`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Let the unknown value be `x`

Then 15% of `x` = 30

In mathematics the of is rather like multiply, so we have:

`15%xx x =30`

`15xx%xx x = 30`

`15/100x=30`

We need to find the value of `x` so if we can change the value of `15/100` to the value of 1 we will have `x` on its own.

`color(brown)("What you do to one side of the equals you do to the other")`

Multiply both sides by `color(red)(100/15)`

`color(green)(15/100color(red)(xx100/15)xx x " "=" " 30color(red)(xx100/15))`

`1xx x=30/15xx100`

`x=2xx 100`

`x=200`