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

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1
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.

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Feb 18, 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

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

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

$\therefore 9 \times 4 = 36$

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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 $\text{Number} = 80$

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