Question

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 3. If there were 7016 total votes, how many novotes were there?no votesх5?

Answer 1

The first thing we have to do is identify our equations that model our problem

`\begin{gathered} total=7016 \\ total=yes+no \\ yes+no=7016\to(1) \end{gathered}`

when they talk to us about the ratio it is a division so

`\begin{gathered} (yes)/(no)=(5)/(3) \\ yes=(5)/(3)no\to(2) \end{gathered}`

Now we have 2 equations we substitute equation (2) in (1) to find the number of no votes

`\begin{gathered} ((5)/(3)no)+no=7016 \\ ((5)/(3)+1)no=7016 \\ (8)/(3)no=7016 \\ no=(7016\cdot3)/(8) \\ no=2631 \end{gathered}`

In total there are 2631 no votes