SOLUTION: In the election for the president of the Graduating Class of the University of Central Florida, 3/5 of the seniors voted for Frank, 3/10 for Steve, and 81 for Nicole. How many seni

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: In the election for the president of the Graduating Class of the University of Central Florida, 3/5 of the seniors voted for Frank, 3/10 for Steve, and 81 for Nicole. How many seni      Log On


   

Question 699501: In the election for the president of the Graduating Class of the University of Central Florida, 3/5 of the seniors voted for Frank, 3/10 for Steve, and 81 for Nicole. How many seniors were there?
Answer by neatmath(302) About Me  (Show Source):
You can put this solution on YOUR website!

I am a graduate of the University of Central Florida!

In this problem, we need to do a bit of investigation.

We have three quantities for the different voters:

3/5, 3/10, and 81

Let's add up the first two groups and see what we get:

3%2F5%2B3%2F10=6%2F10%2B3%2F10=9%2F10

So 9/10 of all the student votes are taken up by the first group.

Then what percentage of all students is left over for Nicole's group?

1-9%2F10=1%2F10

Now we're getting somewhere.

We just need to equate this 1/10 figure to the 81 students.

So let's use x as the TOTAL number of student voters:

%281%2F10%29%2Ax=81

x=81%2A10

x=810

So the total number of student voters should be 810.

Let's check this:

%283%2F5%29%2A810=486

%283%2F10%29%2A810=243

and then our final group of 81. Then:

486%2B243%2B81=810

This is indeed true, so our final answer is 810 Seniors.

I hope this helps! Keep practicing! :)

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