two-fifths of the voters already prefer candidate x. if he took money from a political action committee to buy television time, a third of those who do not now prefer him would be convinced to vote for him. But he would los the support of a fifth of those who support him. If he takes the money, will he win the election, and, what will his shares of the vote be?
I’m lost 2
To determine if Candidate X will win the election and what his share of the vote will be, let's break down the given information step-by-step:
Step 1: Calculation of Current Support
- Start with the total number of voters.
- Let's assume there are 100 voters for simplicity.
- Given that two-fifths of the voters already prefer Candidate X, we can calculate the current support as:
2/5 * 100 = 40 voters prefer Candidate X.
Step 2: Impact of Taking Money from a Political Action Committee (PAC)
- One-third of those who do not currently prefer Candidate X would be convinced to vote for him if he takes money from a PAC.
- This means that one-third of the remaining voters (60 voters who do not currently prefer him) would support him.
1/3 * 60 = 20 voters would now prefer Candidate X.
Step 3: Impact of Losing Support
- Candidate X would lose the support of one-fifth of those who currently support him.
- This implies that one-fifth of his current supporters (40 voters) would no longer prefer him.
1/5 * 40 = 8 voters would no longer prefer Candidate X.
Step 4: Calculation of Final Support
- To determine Candidate X's final support, we add the newly gained supporters and subtract the supporters lost from his current support.
- Final support = Current support + Newly gained supporters - Supporters lost
Final support = 40 (current supporters) + 20 (newly gained supporters) - 8 (supporters lost)
Final support = 52 voters prefer Candidate X.
Step 5: Calculation of Vote Share
- To find Candidate X's share of the vote, divide his final support by the total number of voters.
Vote share = (Final support / Total number of voters) * 100
Vote share = (52 / 100) * 100
Vote share = 52%
Answer:
Based on the given information, if Candidate X takes money from a political action committee (PAC), he will win the election. His share of the vote will be 52%.
To determine if candidate X will win the election and calculate their share of the vote, we need to break down the problem into steps.
Step 1:
Calculate the current number of voters supporting candidate X based on the given information. Since two-fifths of the voters already prefer candidate X, let's assume there are a total of 100 voters. Two-fifths of 100 is (2/5) * 100 = 40. So, candidate X currently has the support of 40 voters.
Step 2:
Calculate the number of voters who do not currently prefer candidate X. Since there are 100 voters in total and we know that 40 voters prefer candidate X, the remaining voters who do not prefer candidate X are 100 - 40 = 60.
Step 3:
Determine the impact of taking money from the political action committee on the votes. If a third of the 60 voters who do not currently prefer candidate X are convinced to vote for him, that would mean 1/3 * 60 = 20 voters will change their preference and support candidate X.
Step 4:
Calculate the updated number of voters supporting candidate X after taking the money. The initial number of supporters was 40, and after gaining 20 new supporters, the new total is 40 + 20 = 60.
Step 5:
Determine the number of supporters who drop their support due to candidate X taking the money. If candidate X loses the support of a fifth of their current supporters, that would be 1/5 * 40 = 8 voters.
Step 6:
Calculate the final number of supporters for candidate X after taking the money. Subtract the supporters who dropped their support from the updated number of supporters. The new total is 60 - 8 = 52 supporters.
Step 7:
To find candidate X's share of the vote, divide the final number of supporters (52) by the total number of voters (100) and multiply by 100 to get the percentage. (52/100) * 100 = 52%. Therefore, candidate X would have a 52% share of the vote.
To summarize, if candidate X takes money from the political action committee to buy television time, they would win the election, and their share of the vote would be 52%.