The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 5 to 7. If there were 5383 no votes, what was the total
number of votes?
The ratio of yes votes (Y) to no votes (N) were 5/7, which means that [tex]\frac{Y}{N}=\frac{5}{7}[/tex].
If there were 5383 no votes N=5383. Then, taking the previous expression, we get [tex]\frac{Y}{N}=\frac{Y}{5383}=\frac{5}{7}[/tex]. From this equivalence we can clear Y (yes votes), [tex]Y=\frac{5}{7}\times5383=3845[/tex]. Then, the yes votes were equal to 3845.
To confirm that the yes votes are well calculated, tou can check that [tex]\frac{Y}{N}=\frac{5}{7}=\frac{3845}{5383}[/tex], which is actually the case.
Finally, the total number of votes is the sum of yes and no votes, [tex]total=3845+5383=9228[/tex]
