math word problem

Question

The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was
4
to
7
. If there were
10,725
total votes, how many no votes were there?

Answer 1

yes:no = 4:7

total = yes + no = 4+7 = 11

 

so, if x = # of no votes

no: total = 7:11 = x:10,725

 

set up a proportion

7/11 = x/10,725      multiply both sides by 10,725

7(10,725)/11 = x  

7(975) = x

6825 = x

 

The number of no votes out of 10,725 total votes is 6825. 

The number of yes votes out of 10,725 total votes is 3900.

 

Check:

yes:no = 3900:6825 = (4×975):(7×975):4:7