# Question c7539

Oct 12, 2017

See explanation

#### Explanation:

10=40%
1=4%
1*25=4*25%
25=100%

Oct 12, 2017

Some explanation in detail

40%" of "25=10

#### Explanation:

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

The symbol % is a bit like a unit of measurement but one that is worth $\frac{1}{100}$

So, in the same way we would say $6 \text{ of } x \to 6 x$
We can say 40" of "%->40%=40xx1/100=40/100

This compares very well to (picking some value at random) $3 c m$

centi $\to \frac{1}{100}$

3 centimetres $\to 3 \times$ centi of 1 metre $\to 3 \times \frac{1}{100} \times 1 \text{ metre}$

$= \frac{3}{100} \text{ metres}$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{b r o w n}{\text{Breaking the question down into its component parts}}$

40% of ...........................40/100xx?

Let the unknown value be represented by $x$ giving:
40% of ...........................$\frac{40}{100} \times x \to \frac{40}{100} x$

10 is ....................................10=?#

10 is 40% of........................$10 = \frac{40}{100} x$

Multiply both sides by $\textcolor{red}{\frac{100}{40}}$
This changes the $\frac{40}{100}$ on the right into 1 so 'getting rid' if it, on that side.

$\textcolor{g r e e n}{10 \textcolor{red}{\times \frac{100}{40}} \textcolor{w h i t e}{\text{d")=color(white)("d}} \frac{40}{100} \textcolor{red}{\times \frac{100}{40}} \times x}$

$\frac{100}{4} = x$

$x = 25$