65% of what number is 26?

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65% of what number is 26?

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Answer 1 · 2016-11-21T10:48:56

$x = 40$ $x=40$

Explanation:

information needed
$65 %$ $65%$ of what number is $26$ $26$ ?

concepts applied
percent to fraction conversion $65 % = \frac{65}{100}$ $65%=65/100$
fractional division $a \div \frac{b}{c} = a \times \frac{c}{b}$ $a\divb/c=a\timesc/b$

calculation

set the number you want to find as $x$ $x$
apply dimensional analysis with conversion factor $\frac{65}{100}$ $65/100$
$\Rightarrow x \times \frac{65}{100} = 26$ $\rArrx\times65/100=26$
divide both sides by $\frac{65}{100}$ $65/100$ $\rArrx\cancel(\times65/100)\cancel(\color(indianred)(\times100/65))=26\color(indianred)(\times100/65)$
simplify multiplication
$\rArrx=(26\times100)/65=2600/65$

solution
$\rArrx=40$

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65% of what number is 26?

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