# 44.64 is %19.9 of x. what is the value of x?

## I don't understand how to get x, and there is no information of the whole percent like what is %19.99 from.

Jan 27, 2018

$\implies x = 224.321$ (approximately.)

#### Explanation:

okkaay, cool.

so the question says, $44.64$ is 19.9% of $x$,

that's like,
19.9% of $x = 44.64 .$

$\implies \frac{19.9}{100} \cdot x = 44.64$

$\implies x = 44.64 \cdot \frac{100}{19.9}$

$\implies x = 224.321$ (approximately.)

Done! :)

-Sahar

Jan 27, 2018

$x = 224.32$

#### Explanation:

The question would be easier to understand if it was written something like this..

If $44.64$ is 19.9% of a number, what is the number?

Remember that the number itself represents 100%

An answer by another contributor shows you the equation method of finding $x$.

Regard it as a proportion.

$44.64$ is to 19.9% as what is to 100%?

44.64/19.9 = x /100" "(larr "numbers")/(larr "percents")

Multiplying by $100$ gives:

$\frac{44.64 \times 100}{19.9} = x$

$x = 224.32$

You can do ANY percentage calculation using direct proportion as long as you match the correct values with the correct percentages.

Jan 27, 2018

$x = 224.32$ to 2 decimal place
Always specify the degree (amount) of rounding.

#### Explanation:

Assumption: you mean 4464 is 19.9% of $x$

$\textcolor{b l u e}{\text{The teaching bit}}$

First lets consider what percentage is.

Basically it is just a fraction but one where the denominator (bottom number) is fixed at 100

There are two ways of writing percentage

The whole fraction itself and just the fractions numerator (top number) followed by the symbol %

How can we relate the % symbol?

By example suppose we had $\frac{20}{100}$

This is the same as $20 \times \frac{1}{100}$

Written the other way we have 20%

So you may if you wish consider % as representing $\times \frac{1}{100}$
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$\textcolor{b l u e}{\text{Answering the question - Full explanation given}}$

Note that in mathematics the word 'of' can normally be translated to multiply. Example: $2 \text{ of } 6 \to 2 \times 6$

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

$44.64$ is ->" "........................44.64=?
19.9% ->" ".........................44.64=19.9/100
of ->" "................................44.64=19.9/100xx?

$x \to \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .44 .64 = \frac{19.9}{100} \times x$

Written as normally seen in mathematics we have:

color(green)(44.64=19.9/100 x

We need to determine the value of $x$ so the objective is to get the $x$ it on its own on one side of the = and everything else on the other side. Thus we need to 'get rid' of the $\frac{19.9}{100}$ on the right. This is done by turning it into 1. Anything multiplied by 1 does not change its value.

Multiply both sides by $\textcolor{red}{\frac{100}{19.9}}$

$\textcolor{g r e e n}{44.64 = \frac{19.9}{100} x \textcolor{w h i t e}{\text{dddd") ->color(white)("ddd}} 44.64 \textcolor{red}{\times \frac{100}{19.9}} = \frac{19.9}{100} x \textcolor{red}{\times \frac{100}{19.9}}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("ddddddddd}} \frac{4464}{19.9} = x \times \frac{19.9}{\textcolor{red}{19.9}} \times \frac{\textcolor{red}{100}}{100}}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{dddddddddddddddd")->color(white)("ddddddddd") 4464/19.9 =x xx color(white)("d")1color(white)("dd")xxcolor(white)("d}} 1}$

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If you use decimals you will not have a precise value answer in this case. So it is better to stick to fractions.

However, the question format is decimal to 2 places. It is customary to give the answer in the same format as the question unless instructed otherwise.

$\frac{4464}{19.9} \times 1 \to \frac{4464}{19.9} \times \frac{10}{10} = \frac{44640}{199}$ as an exact answer

$x = 224.32$ to 1 decimal place (not precise)