Need help with percent word probelm

M

max

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Voting Poll - Candidate A 30%, Candidate B 50%, Undecided 20%

The table above summarizes the results of an election poll ub which 4000 voters participated. In the actual election, all 4000 of these people voted and those people who chose a candidate in the poll voted for that candidate. People who were undecided voted for candidate A in the same proportion as the people who cast votes for candidates in the poll. Of the people polled, how many people voted for candidate A in the actual election?

(a)1420, (b)1500, (c)1640, (d)1680 (e)1800

I have 1200 votes for candidate A, 2000 for candidate B, 800 undecided. I'm lost when it gets to the proportional part.

Can anyone help?
 
30% of 4000 voted for A = .3[4000]= 1200
50% of 4000 voted for B = .5[4000]= 2000
20% of 4000 were undecided= .2[4000]= 800

of the 3200 that voted A received 1200 votes or 1200/3200= 3/8 of voters
then A received of 3/8 of the 800 undecided votes or 300 votes

the total voters A received is 1200 voters plus 300 undecided = 1500 votes
Answer B

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another approach
A and B received 80% of the vote
then A got 30%/80% or 3/8 of the total voted
then B got 50%/80% or 5/8 of the total voted

use which ever method you feel "comfortable" with.

Arthur
 
Proportion of A to B = 0.3/0.5 = 3/5

Thus out of 8 people, who voted for A or B, 3 voted for A and 5 voted for B.

Similarly, now you have 800 people (previously undecided) to divide into A or B (no undecided allowed).

So....
 
Thanks for replies, I believe I understand it.

So the key part was "People who were undecided voted for candidate A in the same proportion as the people who cast votes for candidates in the poll." Which translate to 30%/80% * 800?

In my head I kept trying to make 20% over 80%.
 
yes you are right

You could also say "of those that voted , 3/8 voted for A and 5/8 voted for B".

because the undecided split the same way as thos that voted A received 3/8 of the entire population 3/8x4000 =1500 and B got 5/8 of 4000 = 2500

many ways to skin a cat
Arthur
 
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