how do you solve this word problem?

Question

In a recent election, 45% of the eligible voters actually voted. Of these, 55% voted for the winner.

      a. What percent of eligible voters voted for the winning candidate?

      b. Suppose 495 people voted for the winner. How many eligible voters were there?

Answer 1

|------100 % eligible voters -------------------------------------------|

|-------45% voted------------------|...............55% didn't............|

|--55% winner--|..45% loser..|

 

So hopefully the diagram doesn't get distorted on Wyzant and you can see

that you want to find 55% of 45%  0r (0.55 x 0.45)% of the voters.

 so = 24.75% of eligible voters voted for the winner.

 

Since there were 495 winning voters

24.75% of eligible =  495

therefor 495 / 24.75% is now many eligible voters there were.

 495 /0.2475 =  I am sure you can do the rest.

Answer 2

Part a is talking about both conditions to be satisfied: eligible that voted and vote for winning candidate, therefore you simply need to multiply the percentage. (it is for probability of intersections)

From part a: you should've gotten: 0.45*0.55=0.2475

 

Part b gives you how many eligible voters voted for the winning candidate: 495

Since you already figure the percentage of the eligible voters that voted for the winning candidate. Dividing 495  by 0.2475 will give you the total number of eligible voters.

Hope this helps :)