To determine the percentage increase in the total number of students on the honor roll:
1. Calculate the number of ninth graders on the honor roll this year:
- Last year, there were 72 ninth graders on the honor roll.
- This year there was a 25% increase in ninth graders on the honor roll.
- Increase amount for ninth graders = [tex]\( 72 \times 0.25 = 18 \)[/tex]
- Therefore, the number of ninth graders on the honor roll this year = [tex]\( 72 + 18 = 90 \)[/tex].
2. Calculate the number of tenth graders on the honor roll this year:
- Last year, there were 120 tenth graders on the honor roll.
- This year there was a 5% increase in tenth graders on the honor roll.
- Increase amount for tenth graders = [tex]\( 120 \times 0.05 = 6 \)[/tex]
- Therefore, the number of tenth graders on the honor roll this year = [tex]\( 120 + 6 = 126 \)[/tex].
3. Calculate the total number of students on the honor roll last year and this year:
- Total last year = [tex]\( 72 \)[/tex] (ninth graders) + [tex]\( 120 \)[/tex] (tenth graders) = [tex]\( 192 \)[/tex]
- Total this year = [tex]\( 90 \)[/tex] (ninth graders) + [tex]\( 126 \)[/tex] (tenth graders) = [tex]\( 216 \)[/tex]
4. Determine the increase in the total number of students:
- Increase in total number of students = [tex]\( 216 - 192 = 24 \)[/tex]
5. Calculate the percentage increase:
- Percentage increase = [tex]\( \left( \frac{24}{192} \right) \times 100 \)[/tex]
- Simplifying this, [tex]\( \left( \frac{24}{192} \times 100 \right) = 12.5 \% \)[/tex]
Thus, the percentage increase in the total number of students on the honor roll this year is [tex]\( 12.5 \% \)[/tex].
