Fifty Votes Were Cast In The Class Election Beth Got 1/5 Of The Votes Helen Got As Many Votes Of Those Of Jane And Peter Put Up Together Peter Got 1/3 As Many Votes As Janes How Many Votes Did Each Of The Four Candidates Receive?
Introduction
In a class election, the outcome is often determined by the number of votes each candidate receives. In this scenario, we are given that fifty votes were cast in the class election. We need to determine the number of votes each of the four candidates, Beth, Helen, Jane, and Peter, received. To do this, we will use algebraic equations to represent the given information and solve for the unknowns.
The Given Information
Let's denote the number of votes Jane received as J. Since Peter got 1/3 as many votes as Jane, the number of votes Peter received is (1/3)J. Helen got as many votes as Jane and Peter put up together, so the number of votes Helen received is J + (1/3)J = (4/3)J. Beth got 1/5 of the votes, so the number of votes Beth received is (1/5)(50) = 10.
Setting Up the Equations
We are given that the total number of votes cast in the class election is 50. Therefore, the sum of the votes received by each candidate is equal to 50. We can set up the following equation:
J + (1/3)J + (4/3)J + 10 = 50
Simplifying the Equation
To simplify the equation, we can combine like terms:
(1 + 1/3 + 4/3)J + 10 = 50
Combining the Fractions
To combine the fractions, we need to find a common denominator, which is 3. We can rewrite the fractions as follows:
(3/3 + 1/3 + 4/3)J + 10 = 50
Simplifying the Fractions
Now we can combine the fractions:
(8/3)J + 10 = 50
Subtracting 10 from Both Sides
To isolate the term with J, we can subtract 10 from both sides of the equation:
(8/3)J = 40
Multiplying Both Sides by 3/8
To solve for J, we can multiply both sides of the equation by 3/8:
J = (3/8)(40)
Simplifying the Expression
To simplify the expression, we can multiply 3 and 40:
J = 15
Finding the Number of Votes for Each Candidate
Now that we know the number of votes Jane received, we can find the number of votes for each candidate:
- Jane received 15 votes.
- Peter received (1/3)(15) = 5 votes.
- Helen received (4/3)(15) = 20 votes.
- Beth received 10 votes.
Conclusion
In this scenario, we used algebraic equations to represent the given information and solve for the unknowns. We found that Jane received 15 votes, Peter received 5 votes, Helen received 20 votes, and Beth received 10 votes. This analysis demonstrates the importance of using mathematical techniques to solve real-world problems.
Frequently Asked Questions
- Q: What is the total number of votes cast in the class election? A: The total number of votes cast in the class election is 50.
- Q: How many votes did Jane receive? A: Jane received 15 votes.
- Q: How many votes did Peter receive? A: Peter received 5 votes.
- Q: How many votes did Helen receive? A: Helen received 20 votes.
- Q: How many votes did Beth receive? A: Beth received 10 votes.
Final Answer
The final answer is:
- Jane: 15 votes
- Peter: 5 votes
- Helen: 20 votes
- Beth: 10 votes
Introduction
In our previous article, we analyzed the voting results of a class election where fifty votes were cast. We determined that Jane received 15 votes, Peter received 5 votes, Helen received 20 votes, and Beth received 10 votes. In this article, we will answer some frequently asked questions related to the class election voting.
Q&A
Q: What is the total number of votes cast in the class election?
A: The total number of votes cast in the class election is 50.
Q: How many votes did Jane receive?
A: Jane received 15 votes.
Q: How many votes did Peter receive?
A: Peter received 5 votes.
Q: How many votes did Helen receive?
A: Helen received 20 votes.
Q: How many votes did Beth receive?
A: Beth received 10 votes.
Q: What percentage of the total votes did Jane receive?
A: Jane received 15 votes out of 50, which is (15/50) x 100% = 30%.
Q: What percentage of the total votes did Peter receive?
A: Peter received 5 votes out of 50, which is (5/50) x 100% = 10%.
Q: What percentage of the total votes did Helen receive?
A: Helen received 20 votes out of 50, which is (20/50) x 100% = 40%.
Q: What percentage of the total votes did Beth receive?
A: Beth received 10 votes out of 50, which is (10/50) x 100% = 20%.
Q: Who received the most votes in the class election?
A: Helen received the most votes in the class election with 20 votes.
Q: Who received the least votes in the class election?
A: Peter received the least votes in the class election with 5 votes.
Q: What is the difference between the number of votes received by Helen and Jane?
A: Helen received 20 votes and Jane received 15 votes, so the difference is 20 - 15 = 5 votes.
Q: What is the difference between the number of votes received by Beth and Peter?
A: Beth received 10 votes and Peter received 5 votes, so the difference is 10 - 5 = 5 votes.
Conclusion
In this article, we answered some frequently asked questions related to the class election voting. We provided the total number of votes cast, the number of votes received by each candidate, and the percentage of votes received by each candidate. We also compared the number of votes received by each candidate and calculated the difference between the number of votes received by each pair of candidates.
Final Answer
The final answer is:
- Total number of votes cast: 50
- Number of votes received by each candidate:
- Jane: 15 votes
- Peter: 5 votes
- Helen: 20 votes
- Beth: 10 votes
- Percentage of votes received by each candidate:
- Jane: 30%
- Peter: 10%
- Helen: 40%
- Beth: 20%
- Difference between the number of votes received by each pair of candidates:
- Helen and Jane: 5 votes
- Beth and Peter: 5 votes