# If 39 is 1% of a number, what is that number?

Jun 24, 2018

3900

#### Explanation:

If you think of it logically, this problem is saying:
x*1% = 39
1% is $\frac{1}{100}$ so it's
$x \cdot \frac{1}{100} = 39$
Divide both sides by $\frac{1}{100}$ and you get
$x = \frac{39}{\frac{1}{100}}$
Remember that when there is a fraction in the denominator we flip it and multiply that on top and bottom:
$x = \frac{39 \cdot 100}{\left(\frac{1}{100}\right) \cdot 100}$
Therefore
$x = 3900$

You can check this by multiplying our answer by 1%
$3900 \cdot .01 = 39$

Jun 24, 2018

3900

#### Explanation:

$\textcolor{b l u e}{\text{Method 1: ratio}}$

Note that $\textcolor{m a \ge n t a}{\text{100% is all of it}}$. So we have:

$\textcolor{w h i t e}{\text{d}}$

$\textcolor{p u r p \le}{\text{Initial ratio}}$
$\textcolor{w h i t e}{\text{.dd}} \textcolor{p u r p \le}{\downarrow}$
obrace(" 39 : 1%") ->ubrace(100(39 : 1%))color(white)("d")= color(white)("d")3900:"color(magenta)(100%)
$\textcolor{w h i t e}{\text{dddddddddddddd}} \textcolor{p u r p \le}{\uparrow}$
$\textcolor{p u r p \le}{\text{Multiply everything inside the brackets by 100}}$

$\textcolor{w h i t e}{\text{d}}$

So $\text{39 is 1% of 3900}$

$\textcolor{p u r p \le}{\text{Alternative ratio format in fractional form:}}$

(1%)/39xx100/100 = (100%)/3900

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{b l u e}{\text{Method 2: algebraic manipulation}}$

Set the unknown value as $x$

Known that 1% is the same as $\frac{1}{100}$

Then $\frac{1}{100} \times x = 39$

Multiply both sides by $\textcolor{red}{\frac{100}{1}}$

color(green)(1/100xx x = 39 color(white)("ddd")-> color(white)("ddd")1/cancel(100)^1 color(red)(xx cancel(100)^1/1)xx x =39 xx color(red)(100/1)

$\textcolor{w h i t e}{\text{dddddddddddddd")->color(white)("dddddddddddddddddd}} x = 3900$