# 30 is 15% of what number?

Feb 9, 2016

$200$

#### Explanation:

Let $x$ be the number:

Then,

$\rightarrow \frac{15}{100} \left(x\right) = 30$

$\rightarrow \frac{3}{20} \left(x\right) = 30$

$\rightarrow \frac{3 x}{20} = 30$

$\rightarrow 3 x = 20 \cdot 30$

$\rightarrow 3 x = 600$

$\rightarrow x = \frac{600}{3} = 200$

Mar 23, 2017

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

30 is 15% of 200

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

You can think of % as a sort of unit of measurement but one that is worth $\frac{1}{100}$

So 15%" "->" "15xx%" "->" "15xx1/100=15/100
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$\textcolor{b l u e}{\text{Answering the question}}$

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

$\frac{15}{100} x = 30$

We need to find the value of $x$ so if we can change the value of $\frac{15}{100}$ to the value of 1 we will have $x$ on its own.

$\textcolor{b r o w n}{\text{What you do to one side of the equals you do to the other}}$

Multiply both sides by $\textcolor{red}{\frac{100}{15}}$

$\textcolor{g r e e n}{\frac{15}{100} \textcolor{red}{\times \frac{100}{15}} \times x \text{ "=" } 30 \textcolor{red}{\times \frac{100}{15}}}$

$1 \times x = \frac{30}{15} \times 100$

$x = 2 \times 100$

$x = 200$