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Last year at a certain high school, there were 52 ninth graders on the honor roll and 150 tenth graders on the honor roll. This year, the number of ninth graders on the honor roll decreased by 25% and the number of tenth graders on the honor roll decreased by 2%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary). Answer:

Last year at a certain high school, there were 5252 ninth graders on the honor roll and 150150 tenth graders on the honor roll. This year, the number of ninth graders on the honor roll decreased by 25% 25 \% and the number of tenth graders on the honor roll decreased by 2% 2 \% . By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).\newlineAnswer:

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Q. Last year at a certain high school, there were 5252 ninth graders on the honor roll and 150150 tenth graders on the honor roll. This year, the number of ninth graders on the honor roll decreased by 25% 25 \% and the number of tenth graders on the honor roll decreased by 2% 2 \% . By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary).\newlineAnswer:
  1. Calculate Decrease Ninth Graders: First, let's calculate the decrease in the number of ninth graders on the honor roll. We know that the number of ninth graders on the honor roll decreased by 25%25\%. To find out how many ninth graders are no longer on the honor roll, we calculate 25%25\% of 5252.\newlineDecrease in ninth graders = 25%25\% of 5252 = 0.25×52=130.25 \times 52 = 13
  2. Calculate New Ninth Graders: Now, let's calculate the new number of ninth graders on the honor roll after the decrease.\newlineNew number of ninth graders on honor roll = Original number - Decrease = 52−13=3952 - 13 = 39
  3. Calculate Decrease Tenth Graders: Next, we calculate the decrease in the number of tenth graders on the honor roll. The number of tenth graders on the honor roll decreased by 2%2\%. To find out how many tenth graders are no longer on the honor roll, we calculate 2%2\% of 150150.\newlineDecrease in tenth graders = 2%2\% of 150150 = 0.02×1500.02 \times 150 = 33
  4. Calculate New Tenth Graders: Now, let's calculate the new number of tenth graders on the honor roll after the decrease.\newlineNew number of tenth graders on honor roll = Original number - Decrease = 150−3=147150 - 3 = 147
  5. Calculate Total Students: We now have the new numbers of ninth and tenth graders on the honor roll. To find the total number of students on the honor roll this year, we add the numbers together.\newlineTotal number of students on honor roll this year = New number of ninth graders + New number of tenth graders = 39+147=18639 + 147 = 186
  6. Calculate Total Last Year: To find the original total number of students on the honor roll last year, we add the original numbers of ninth and tenth graders together.\newlineTotal number of students on honor roll last year == Original number of ninth graders ++ Original number of tenth graders =52+150=202= 52 + 150 = 202
  7. Calculate Total Decrease: Now, let's calculate the total decrease in the number of students on the honor roll.\newlineTotal decrease = Original total - New total = 202−186=16202 - 186 = 16
  8. Calculate Percentage Decrease: Finally, to find the percentage decrease in the total number of students on the honor roll, we divide the total decrease by the original total and multiply by 100100.\newlinePercentage decrease = (Total decrease/Original total)×100=(16202)×100(\text{Total decrease} / \text{Original total}) \times 100 = (\frac{16}{202}) \times 100\newlinePercentage decrease ≈7.92%\approx 7.92\%
  9. Round Percentage Decrease: We round the percentage decrease to the nearest tenth.\newlineRounded percentage decrease = 7.9%7.9\%

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