30 is 15% of what number?

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Answer 1 · 2016-02-09T12:22:17

$200$

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 · 2017-03-23T18:41:29

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

30 is 15% of 200

$color(blue)("Preamble")$

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 $color(red)(100/15)$

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

$1xx x=30/15xx100$

$x=2xx 100$

$x=200$