Question
Students voted for a new class president and the results are shown in the table.
A 2-column table with 3 rows. Column 1 is labeled Candidate with entries Rosalia, Jocelyn, Danny. Column 2 is labeled Votes with entries 124, 109, 111.
Suppose four more people voted and they all voted for Jocelyn. What fraction of the votes would be for Jocelyn?
A 2-column table with 3 rows. Column 1 is labeled Candidate with entries Rosalia, Jocelyn, Danny. Column 2 is labeled Votes with entries 124, 109, 111.
Suppose four more people voted and they all voted for Jocelyn. What fraction of the votes would be for Jocelyn?
Answers
GPT-4o mini
To determine the new fraction of votes for Jocelyn after four additional votes, we start with the initial vote counts:
- Rosalia: 124 votes
- Jocelyn: 109 votes
- Danny: 111 votes
First, let's calculate the total initial number of votes:
Total initial votes = Rosalia's votes + Jocelyn's votes + Danny's votes
Total initial votes = 124 + 109 + 111 = 344
Next, we add the four new votes for Jocelyn:
New votes for Jocelyn = 109 + 4 = 113
Now we calculate the new total number of votes:
Total new votes = Total initial votes + New votes
Total new votes = 344 + 4 = 348
Next, we find the fraction of votes for Jocelyn:
Fraction of votes for Jocelyn = (New votes for Jocelyn) / (Total new votes)
Fraction of votes for Jocelyn = 113 / 348
To simplify the fraction, we can find the greatest common divisor (GCD) of 113 and 348. However, since 113 is a prime number, we can check if it divides 348:
348 ÷ 113 ≈ 3.08 (not divisible)
Since 113 does not divide 348, the fraction is already in its simplest form.
Thus, the fraction of votes that would be for Jocelyn after the four additional votes is:
\[
\frac{113}{348}
\]
- Rosalia: 124 votes
- Jocelyn: 109 votes
- Danny: 111 votes
First, let's calculate the total initial number of votes:
Total initial votes = Rosalia's votes + Jocelyn's votes + Danny's votes
Total initial votes = 124 + 109 + 111 = 344
Next, we add the four new votes for Jocelyn:
New votes for Jocelyn = 109 + 4 = 113
Now we calculate the new total number of votes:
Total new votes = Total initial votes + New votes
Total new votes = 344 + 4 = 348
Next, we find the fraction of votes for Jocelyn:
Fraction of votes for Jocelyn = (New votes for Jocelyn) / (Total new votes)
Fraction of votes for Jocelyn = 113 / 348
To simplify the fraction, we can find the greatest common divisor (GCD) of 113 and 348. However, since 113 is a prime number, we can check if it divides 348:
348 ÷ 113 ≈ 3.08 (not divisible)
Since 113 does not divide 348, the fraction is already in its simplest form.
Thus, the fraction of votes that would be for Jocelyn after the four additional votes is:
\[
\frac{113}{348}
\]