According to an informal poll in Glenview, 1/3 of the men and 2/3 of the women saud they would vote for John Smith. On election day, one and a half times as many men as women voted. What fraction of the total vote, according to the poll, should be cast for John Smith?
Since there were 1.5 times as many men as women voting, 60% of the votes were by me and 40% by women.
The fraction of all votes that were for Smith was therefore:
0.6*(1/3) + 0.4(2/3) = 6/30 + 8/30 = 14/30 = 46.7%
Well, if we're dealing with fractions, we'll need to put on our thinking caps and do some math-trickery! Let's dive in, shall we?
According to the poll, 1/3 of men and 2/3 of women said they would vote for John Smith. So, if we assume there are 3 men and 3 women, that means 1 man and 2 women would vote for John Smith.
Now, on election day, the number of men who voted is one and a half times the number of women who voted. If we let the number of women be x, then the number of men who voted would be 1.5x.
So, the total number of people who voted for John Smith would be 1 + (1.5x) + 2x, which simplifies to 1 + 3.5x.
But wait, there's more! We also need to take into account the total number of votes cast. Since we assumed there were 3 men and 3 women, the total number of votes cast would be 3 + 3 = 6.
To find the fraction of the total vote cast for John Smith, we'll divide the number of votes for John Smith (1 + 3.5x) by the total number of votes cast (6):
(1 + 3.5x) / 6.
Now, this fraction will give you the answer you're looking for, based on the assumptions we made. Just plug in the appropriate numbers, and you'll have your solution! Voila!
To solve this problem, let's first assume that there are 3 men and 3 women in Glenview.
According to the poll:
- 1/3 of the men (1 man) said they would vote for John Smith.
- 2/3 of the women (2 women) said they would vote for John Smith.
Now, on election day, we are given that one and a half times as many men as women voted. Therefore, there are 1.5 * 3 = 4.5 men who voted (since we cannot have half a person, we consider this as 4 men) and 3 women who voted.
So, the total number of votes cast for John Smith would be 1 (man) + 2 (women) = 3 votes.
Since we assumed there are 3 men and 3 women, the total number of votes would be 6 (3 men + 3 women).
The fraction of the total vote cast for John Smith, according to the poll, would be 3/6 = 1/2.
Therefore, according to the poll, 1/2 of the total vote should be cast for John Smith.
To determine the fraction of the total vote that should be cast for John Smith, we need to calculate the number of votes each gender will contribute and then find the fraction that corresponds to John Smith's share of the votes.
Let's assume there are 100 men and 100 women in Glenview for simplicity.
Based on the poll, 1/3 of the men in Glenview would vote for John Smith. So, the number of votes John Smith would receive from men is (1/3) * 100 = 33.
Similarly, 2/3 of the women would vote for John Smith. Therefore, the number of votes John Smith would receive from women is (2/3) * 100 = 66.
On election day, one and a half times as many men as women voted. So, the number of men who voted would be (1.5) * 100 = 150, and the number of women who voted would be 100.
Now, let's calculate the total number of votes cast for John Smith. The total votes John Smith would receive would be the sum of the votes from men and women, which is 33 (from men) + 66 (from women) = 99.
Finally, we need to find the fraction of the total vote that John Smith received. The total number of votes is the sum of the votes from men (150) and women (100), which is 150 + 100 = 250.
Therefore, the fraction of the total vote cast for John Smith, according to the poll, is 99/250.
Note: This calculation assumes that the number of men and women in Glenview is equal, which makes it easier to illustrate the concept. In reality, the actual numbers might differ, but the approach remains the same.