# 65% of what number is 26?

Nov 21, 2016

$x = 40$

#### Explanation:

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

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

calculation

• set the number you want to find as $x$
• apply dimensional analysis with conversion factor $\frac{65}{100}$
$\setminus \Rightarrow x \setminus \times \frac{65}{100} = 26$
• divide both sides by $\frac{65}{100}$ $\setminus \Rightarrow x \setminus \cancel{\setminus \times \frac{65}{100}} \setminus \cancel{\setminus \textcolor{\in \mathrm{di} a n red}{\setminus \times \frac{100}{65}}} = 26 \setminus \textcolor{\in \mathrm{di} a n red}{\setminus \times \frac{100}{65}}$
• simplify multiplication
$\setminus \Rightarrow x = \frac{26 \setminus \times 100}{65} = \frac{2600}{65}$

solution
$\setminus \Rightarrow x = 40$