Last year at a certain high school, there were $150$ ninth graders on the honor roll and $100$ tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by $20\%$ and the number of tenth graders on the honor roll increased by $3\%$ . By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

View step-by-step help

Home

Math Problems

Algebra 1

Exponential growth and decay: word problems

Full solution

Q. Last year at a certain high school, there were

150

ninth graders on the honor roll and

100

tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by

20\%

and the number of tenth graders on the honor roll increased by

3\%

. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).

Calculate new ninth graders: Calculate the new number of ninth graders on the honor roll after a $20$ % increase. $\newline$ The original number of ninth graders on the honor roll was $150$ . To find the new number, we calculate $20\%$ of $150$ and add it to the original number. $\newline$ $20\%$ of $150$ = $0.20 \times 150$ = $30$ $\newline$ New number of ninth graders on the honor roll = $150 + 30$ = $180$
Calculate new tenth graders: Calculate the new number of tenth graders on the honor roll after a $3\%$ increase. $\newline$ The original number of tenth graders on the honor roll was $100$ . To find the new number, we calculate $3\%$ of $100$ and add it to the original number. $\newline$ $3\%$ of $100$ = $0.03 \times 100 = 3$ $\newline$ New number of tenth graders on the honor roll = $100 + 3 = 103$
Calculate total last year: Calculate the total number of students on the honor roll last year. $\newline$ Total number of students on the honor roll last year $=$ number of ninth graders $+$ number of tenth graders $\newline$ $= 150 + 100 = 250$
Calculate total this year: Calculate the total number of students on the honor roll this year. $\newline$ Total number of students on the honor roll this year $=$ new number of ninth graders $+$ new number of tenth graders $\newline$ $= 180 + 103 = 283$
Calculate increase: Calculate the increase in the total number of students on the honor roll. $\newline$ Increase in the total number of students $=$ total this year $-$ total last year $\newline$ $= 283 - 250 = 33$
Calculate percentage increase: Calculate the percentage increase in the total number of students on the honor roll. $\newline$ Percentage increase = $(\frac{\text{increase in the total number}}{\text{total last year}}) \times 100$ $\newline$ = $(\frac{33}{250}) \times 100$ $\newline$ = $0.132 \times 100$ $\newline$ = $13.2\%$