Last year at a certain high school, there were 120 ninth graders on the honor roll and 105 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 20%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary). Answer:

Question

Last year at a certain high school, there were 120 ninth graders on the honor roll and 105 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  20%. By what percentage did the total number of students on the honor roll decrease? Round your answer to the nearest tenth (if necessary). Answer:

Bytelearn · Accepted Answer

Calculate New Number: Calculate the new number of ninth graders on the honor roll after a 25% decrease. Original number of ninth graders on the honor roll: 120 Percentage decrease: 25% New number of ninth graders = 120 - (25% of 120) = 120 - (0.25 × 120) = 120 - 30 = 90Calculate New Number: Calculate the new number of tenth graders on the honor roll after a 20% decrease. Original number of tenth graders on the honor roll: 105 Percentage decrease: 20% New number of tenth graders = 105 - (20% of 105) = 105 - (0.20 × 105) = 105 - 21 = 84Calculate Total Last Year: Calculate the total number of students on the honor roll last year. Total last year = Number of ninth graders + Number of tenth graders = 120 + 105 = 225Calculate Total This Year: Calculate the total number of students on the honor roll this year. Total this year = New number of ninth graders + New number of tenth graders = 90 + 84 = 174Calculate Decrease: Calculate the decrease in the total number of students on the honor roll. Decrease in total = Total last year - Total this year = 225 - 174 = 51Calculate Percentage Decrease: Calculate the percentage decrease in the total number of students on the honor roll. Percentage decrease = (Decrease in total / Total last year) × 100% = (51 / 225) × 100% = 0.2266... × 100% = 22.666...% Round to the nearest tenth: 22.7%

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