Of the students attending a school athletic event, $80\%$ of the boys were dressed in the school colors, $60\%$ of the girls were dressed in the school colors, and $45\% $ of the students were girls. Find the percentage of students attending the event who were wearing the school colors.
1. **Define Variables and Given Information:**
   - Let the total number of students be \( N \).
   - Let the number of girls be \( G \).
   - Let the number of boys be \( B \).
   - Given that \( 45\% \) of the students are girls, we have:
     \[
     G = 0.45N
     \]
   - Therefore, the number of boys is:
     \[
     B = N - G = N - 0.45N = 0.55N
     \]

2. **Calculate the Number of Girls and Boys Wearing School Colors:**
   - \( 60\% \) of the girls were dressed in school colors:
     \[
     \text{Girls in school colors} = 0.60G = 0.60 \times 0.45N = 0.27N
     \]
   - \( 80\% \) of the boys were dressed in school colors:
     \[
     \text{Boys in school colors} = 0.80B = 0.80 \times 0.55N = 0.44N
     \]

3. **Calculate the Total Number of Students Wearing School Colors:**
   - The total number of students wearing school colors is the sum of the girls and boys wearing school colors:
     \[
     \text{Total in school colors} = 0.27N + 0.44N = 0.71N
     \]

4. **Calculate the Percentage of Students Wearing School Colors:**
   - The percentage of students wearing school colors is:
     \[
     \frac{\text{Total in school colors}}{N} \times 100\% = \frac{0.71N}{N} \times 100\% = 71\%
     \]

The final answer is \(\boxed{71\%}\)