Percentage

[jcnissi]

In a certain voting district, 40 percent of the registered voters live in Town A and the rest live in Town B. In the last election, 70 percent of the registered voters from Town A voted. If equal numbers of registered voters from both towns voted, approximately what percent of the registered voters from Town B voted?

a. 72%
b. 47%
c. 42%
d. 34%
e. 28%

[Rich@VeritasPrep]

In any percentage question like this (in which there is an unspecified quantity), it helps to plug in 100.

Use 100 as the number of registered voters.

So that means...

40 voters in Town A
60 voters in Town B

.7(40) = 28 voters from A voted

Therefore, 28 voters from town B voted, since "equal numbers of registered voters from both towns voted".

28 voters out of 60 voted from Town B, therefore...

28/60 = 7/15 of the voters of Town B voted.

At this point, you can eliminate A, D, and E, because 7/15 is only slightly less than 50%.

Most likely, it will be B, and it turns out it is. You can verify this with a little long division or a proportion:

7/15 = x/100

Another way you could look at it:

The number of voters who voted in each town is equal, so you could go straight to this equation:

70% of 40 voters = x% of 60 voters

.7(40) = (x/100)(60)

28 = 60x / 100

28 = 3x / 5

140 = 3x

140/3 = x

x = [spoiler]46.6666666... ~= 47[/spoiler]


Hope that helps! Let me know if anything needs clarification.

[jcnissi]

Thanks so much for the detailed description. I like to understand the problem conceptually and this helps a lot!