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?

Answer 1

To find out the new fraction of votes for Jocelyn after four more votes are cast for her, we start with the original votes:

- Rosalia: 124 votes
- Jocelyn: 109 votes
- Danny: 111 votes

First, we calculate the total number of votes before the additional votes:

\[
\text{Total Votes} = 124 + 109 + 111 = 344
\]

Now, we add the 4 new votes for Jocelyn:

\[
\text{New Votes for Jocelyn} = 109 + 4 = 113
\]

Now we can find the new total number of votes:

\[
\text{New Total Votes} = 344 + 4 = 348
\]

Next, we calculate the fraction of votes that are for Jocelyn:

\[
\text{Fraction of Votes for Jocelyn} = \frac{\text{Votes for Jocelyn}}{\text{Total Votes}} = \frac{113}{348}
\]

To simplify this fraction, we can check if there are any common factors between 113 and 348. Since 113 is a prime number, we will divide both the numerator and denominator by the greatest common divisor (GCD).

The GCD of 113 and 348 is 1, which means the fraction cannot be simplified further. Therefore, the fraction of the votes for Jocelyn, after the additional votes are counted, is:

\[
\frac{113}{348}
\]

Thus, after four more people vote for Jocelyn, the fraction of votes for Jocelyn is \(\frac{113}{348}\).