People attending a football game either supported the home team or the visiting team. If 714 of the people attending supported the home team and 2686 supported the visiting team, what percentage supported the home team?

21%

Step-by-step explanation:

First find the whole, the total number of attendees:

714 \text{ home} + 2686 \text{ visiting} = \color{orange}{3400} \text{ total attendees}

714 home+2686 visiting=3400 total attendees

Method 1: Set up a proportion

Set up an equation of the form:

\frac{\color{red}{\text{part}}}{\color{orange}{\text{whole}}}=

whole

part

=

\,\,\frac{\color{blue}{\text{percent}}}{100}

100

percent

Assign the variable xx to the unknown value:

\color{blue}{x}=

x=

\,\,\color{blue}{\text{percent}}

percent

The question asks what \textit{percent}percent of all the attendees is 714

Substitute the known values with the numbers given in the problem, and the unknown value with xx:

\frac{\color{red}{714}}{\color{orange}{3400}}=

3400

714

=

\,\,\frac{\color{blue}{x}}{100}

100

x

Solve for xx:

100\cdot\color{red}{714}=

100⋅714=

\,\,\color{orange}{3400}\cdot\color{blue}{x}

3400⋅x

Cross multiply

\frac{71400}{3400}=

3400

71400

=

\,\,\frac{3400x}{3400}

3400

3400x

Divide both sides by 100

\color{blue}{21\%}=

21%=

\,\,\color{blue}{x}

x

Simplify

Method 2: Find percent directly

\text{Find \(714\) out of \(3400\) as a decimal:}

Find 714 out of 3400 as a decimal:

\frac{\color{red}{714}}{\color{orange}{3400}}=

3400

714

=

\,\,0.21

0.21

\text{Convert decimal to percent:}

Convert decimal to percent:

0.21\times100=

0.21×100=

\,\,\color{blue}{21\%}

21%

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