Question

Suppose 123 people voted for Danny. If 55 of the votes were from girls, what would be the ratio of votes from girls to votes from boys? Explain.

Answer 1

To determine the ratio of votes from girls to votes from boys, we first need to find out how many votes came from boys.

Given:
- Total votes for Danny = 123
- Votes from girls = 55

To find the votes from boys, we subtract the votes from girls from the total votes:

\[
\text{Votes from boys} = \text{Total votes} - \text{Votes from girls} = 123 - 55 = 68
\]

Now, we have:
- Votes from girls = 55
- Votes from boys = 68

Next, we can set up the ratio of votes from girls to votes from boys:

\[
\text{Ratio of votes from girls to votes from boys} = \frac{\text{Votes from girls}}{\text{Votes from boys}} = \frac{55}{68}
\]

To simplify this ratio, we can find the greatest common divisor (GCD) of 55 and 68. The GCD is 1 (as 55 is 5 * 11 and 68 is 4 * 17, with no common factors).

Thus, the simplified ratio remains:

\[
\frac{55}{68}
\]

Therefore, the ratio of votes from girls to votes from boys is:

\[
\mathbf{55:68}
\]