# The 60% length of a road is 75 km. How do you find the total length of the road?

Dec 26, 2016

The total length of the road is 125 km

#### Explanation:

We can rewrite this problem as:

60% of what is 75 km?

"Percent" or "%" means "out of 100" or "per 100", Therefore 60% can be written as $\frac{60}{100}$.

When dealing with percents the word "of" means "times" or "to multiply".

Finally, lets call the number we are looking for "l".

Putting this altogether we can write this equation and solve for $l$ while keeping the equation balanced:

$\frac{60}{100} \times l = 75 k m$

$\frac{100}{60} \times \frac{60}{100} \times l = \frac{100}{60} \times 75 k m$

$\frac{\textcolor{red}{\cancel{100}}}{\textcolor{b l u e}{\cancel{60}}} \times \frac{\textcolor{b l u e}{\cancel{60}}}{\textcolor{red}{\cancel{100}}} \times l = \frac{7500}{60} k m$

$l = 125 k m$

Dec 26, 2016

$125$

#### Explanation:

Let the total length of the road be $x$
60%=60/100=0.6
$\implies x \times 0.6 = 75$
$\implies x = \frac{75}{0.6} = 125$