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

$\begin{gathered} \frac{yes}{no}=\frac{5}{3} \\ yes=\frac{5}{3}no\to(2) \end{gathered}$

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

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

In total there are 2631 no votes