# If 45% of a number is 36, what is the number?

Feb 14, 2017

Number is $80$

#### Explanation:

As 45% of a number is $36$,

45%xx"Number"=36

or $\frac{45}{100} \times \text{Number} = 36$

or $\frac{45}{100} \times \frac{100}{45} \times \text{Number} = 36 \times \frac{100}{45}$

or ${\cancel{45}}^{1} / {\cancel{100}}^{1} \times {\cancel{100}}^{1} / {\cancel{45}}^{1} \times \text{Number} = {\cancel{36}}^{4} \times \frac{100}{\cancel{45}} ^ 5$

or $\text{Number} = \frac{4 \times {\cancel{100}}^{20}}{{\cancel{5}}^{1}}$

or $\text{Number} = 80$

Feb 14, 2017

$80$

#### Explanation:

Let the number be $x$

45% of $x = 36$

45% of $x$ can also be written as 45% xx x

$\frac{45}{100} \times x = 36$

$0.45 x = 36$

$x = \frac{36}{0.45} .$

$x = 80$

check:

:.45% xx 80

$\therefore {\cancel{45}}^{9} / {\cancel{100}}^{20} \times 80$

$\therefore \frac{9}{\cancel{20}} ^ 1 \times {\cancel{80}}^{4} / 1$

$\therefore 9 \times 4 = 36$

Feb 16, 2017

The number is $80$

#### Explanation:

Percentage questions can always be done by a direct proportion method, which is the same as using equivalent fractions.

In this case we are told that 36 is 45% of a certain number. The number itself would represent 100%

If we use $x$ for the number, we have:

$\frac{36}{45} = \frac{x}{100} \text{ } \leftarrow$ "If 36 is 45%, how much is 100%?"

$45 x = 36 \times 100 \text{ } \leftarrow$ cross multiply

$x = \frac{36 \times 100}{45}$

$x = 80$

This method is particularly useful with reverse percentages.

Jun 1, 2017

The number is 80!

#### Explanation:

Whenever I come across these kind of questions, I use a formula. $x$ will represent the number because we don't know the number yet. For this case, the formula would be,
$x$$\setminus \cdot$$\frac{45}{100}$$=$$36$.

The value of $x$ will be the answer. So let's start!

$x$$\setminus \cdot$$\frac{45}{100}$$=$$36$

$x$$=$$36$$\setminus \cdot$$\frac{100}{45}$ (Leave $x$ on one side)

$x$$=$${\cancel{36}}^{4} / 1$$\setminus \cdot$$\frac{100}{\cancel{45}} ^ 5$ (Multiply)

$x$$=$$\frac{400}{5}$ (Simplify)

$x$$=$$80$

Did you know that in mathematics, of means $\times$ and/or $\cdot$! So 45% of $80$ is,

$\frac{45}{100}$$\times$$80$!

Let's check if the answer is correct!

$\frac{45}{100}$$\times$$\frac{80}{1}$

$=$$\frac{45}{\cancel{100}} ^ 5$$\times$${\cancel{80}}^{4} / 1$

$=$$\frac{180}{5}$

$=$$36$

I learned how to type the multiplication sign (dot) here! That's one source, and my other source is my brain!
Now since we checked the answer, we know that $80$ is correct!
I hope that helps and that you understood it!

All the best,
Moksha :D