# In a recent survey, 216 people of 54% of the same said they usually went to a family restaurant when they went out to eat. How many people were surveyed?

Mar 20, 2017

See the entire solution process below:

#### Explanation:

We can rewrite this problem as:

#216 is 54% of how many people?

"Percent" or "%" means "out of 100" or "per 100", Therefore 54% can be written as $\frac{54}{100}$.

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

Finally, lets call the number of people we are looking for "p".

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

$216 = \frac{54}{100} \times p$

$\frac{\textcolor{red}{100}}{\textcolor{b l u e}{54}} \times 216 = \frac{\textcolor{red}{100}}{\textcolor{b l u e}{54}} \times \frac{54}{100} \times p$

$\frac{21600}{\textcolor{b l u e}{54}} = \frac{\cancel{\textcolor{red}{100}}}{\cancel{\textcolor{b l u e}{54}}} \times \frac{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{54}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{100}}}} \times p$

$400 = p$

216 is 54% of $\textcolor{red}{400}$ people surveyed