# In a survey, 27% of the people chose salads over a meat dish. In all, 81 people chose salads. How many people were in the survey?

Nov 21, 2015

300 people in total

#### Explanation:

Let the total number of people by $x$
Let number choosing salad be $s$
Let number choosing meat be $m$

Word group by word group:

27% of the peoples chose salad:
$s = \frac{27}{100} x$

In all, 81 people chose salad:

$s = \frac{27}{100} x = 81. \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left(1\right)$

Meat does not come into the equation!!!

Multiply both sides of equation (1) by $\textcolor{b l u e}{\frac{100}{27}}$

$\textcolor{b r o w n}{\left(\frac{27}{100} x\right)} \times \textcolor{b l u e}{\frac{100}{27}} = \textcolor{b r o w n}{\left(81\right)} \times \textcolor{b l u e}{\frac{100}{27}}$

$\textcolor{g r e e n}{\text{The brackets serve no purpose other than to show you what}}$
$\textcolor{g r e e n}{\text{is being altered or for grouping to make what is happening clearer.}}$

$\frac{\textcolor{b r o w n}{27} \times \textcolor{b l u e}{100}}{\textcolor{b r o w n}{100} \times \textcolor{b l u e}{27}} \times \textcolor{b r o w n}{x} = \textcolor{b r o w n}{81} \times \textcolor{b l u e}{\frac{100}{27}}$

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But $\frac{27 \times 100}{100 \times 27} \equiv \frac{27}{27} \times \frac{100}{100} = 1 \times 1$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
So we have:

$1 \times 1 \times x = \frac{81 \times 100}{27}$

$x = \frac{81 \times 100}{27} = 300$

To really polish off this answer and get good marks you would need to define the unit of measurement or count. Which is people. So you could write something like:

## $\textcolor{g r e e n}{\text{The total number of people is 300}}$

Dec 5, 2016

300 people is absolutely right answer.

#### Explanation:

It can be further simply explained as under :-

Percent means per 100 numbers of unit

so 27 % means 27 numbers people out of per 100 Number people

Since 27 people chose salad out of 100 Number people
so what numbers of total people if 81 people choose in actual

27 Nos from 100 Number
81 Nos ???

$100 \cdot \frac{81}{27} = 300$

Answer is total number of people is 300

[ The previous answer and explanation is perfectly right, it is just a alternative and quick method to find out the answer]