In an election, Kate lost to Lee by 32 votes. Because the vote was so close, they decided to have a re-vote. All of Kate's supporters voted fro her again, but some of Lee's supporters switched their votes to vote for Kate. Kate won by the revote by 6 votes. How may of Lee's original supporters voted for Kate.
original vote:
kate ---- x
lee ------x+32
new vote: number of swing votes --- y
kate --- x+y
lee -----x+32 - y
kate - lee = 6
x+y - (x+32-y) = 6
x+y-x-32x+xy = 6
2y = 38
y = 19
19 voters switched
To find the number of Lee's original supporters who voted for Kate in the re-vote, we need to work backwards from the given information.
Let's assume that in the original election, Kate had x number of votes and Lee had y number of votes.
Given that Kate lost to Lee by 32 votes, we can write the equation:
y - x = 32 ........(equation 1)
In the re-vote, Kate won by 6 votes. That means the difference between the number of votes she received and the number of votes Lee received in the re-vote is 6. Since some of Lee's supporters switched their votes to Kate, we can adjust the equation as:
x + (y - Lee's supporters who switched their votes) = Kate's votes in the re-vote
Given that Kate won the re-vote by 6 votes, we can write the equation:
x + (y - Lee's supporters who switched their votes) - y = 6 ......(equation 2)
Simplifying equation 2, we get:
x - Lee's supporters who switched their votes = 6 .....(equation 3)
We can solve equations 1 and 3 simultaneously to find the values of x and y.
From equation 1, we have:
y = x + 32
Substituting this value of y in equation 3, we get:
x - Lee's supporters who switched their votes = 6
x - (x + 32) = 6
x - x - 32 = 6
-32 = 6
This is not a possible solution as -32 cannot equal 6.
Hence, there must be an error in the information provided or in the question itself. Please recheck the given information or provide additional details so that we can help you find the correct answer.