1. **State the problem:** We have 150 ninth graders and 75 tenth graders on the honor roll last year. This year, ninth graders decreased by 8% and tenth graders decreased by 20%. We need to find the overall percentage decrease in the total number of students on the honor roll. 2. **Write down the initial totals:** - Ninth graders last year: $150$ - Tenth graders last year: $75$ - Total last year: $150 + 75 = 225$ 3. **Calculate the number of students this year:** - Ninth graders decreased by 8%, so remaining is $100\% - 8\% = 92\% = 0.92$ - Tenth graders decreased by 20%, so remaining is $100\% - 20\% = 80\% = 0.80$ 4. **Calculate this year's numbers:** - Ninth graders this year: $150 \times 0.92 = 138$ - Tenth graders this year: $75 \times 0.80 = 60$ - Total this year: $138 + 60 = 198$ 5. **Calculate the decrease in total students:** - Decrease amount: $225 - 198 = 27$ 6. **Calculate the percentage decrease:** $$\text{Percentage decrease} = \frac{\text{Decrease}}{\text{Original total}} \times 100 = \frac{27}{225} \times 100$$ 7. **Simplify the fraction:** $$\frac{27}{225} = \frac{\cancel{27}^1}{\cancel{225}^8.333...}$$ Since 225 divided by 27 is 8.333..., better to calculate decimal: $$\frac{27}{225} = 0.12$$ 8. **Calculate the percentage:** $$0.12 \times 100 = 12\%$$ 9. **Round to the nearest tenth:** The answer is $12.0\%$. **Final answer:** The total number of students on the honor roll decreased by **12.0%** this year.