Question

Last year at a certain high school, there were 150 boys on the honor roll and 150 girls

on the honor roll. This year, the number of boys on the honor roll increased by 24%
and the number of girls on the honor roll increased by 6%. By what percentage did
the total number of students on the honor roll increase? Round your answer to the
nearest tenth (if necessary).

Answer 1

15%

Explanation:

The percentage increase can be found by dividing the increase by the original number.

Application

The increase in the number of boys was ...

24% × 150

The increase in the number of girls was ...

6% × 150

So, the total increase in the number of honor roll students was ...

24% × 150 + 6% × 150 = (24% +6%) × 150 = 30% × 150 . . . increase

The original number of honor roll students was ...

150 (boys) +150 (girls) = 300

Then the overall percentage increase in the number of honor roll students was ...

`(30\%*150)/(300)=(30\%)/(2)=\boxed{15\%}`

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Additional comment

Essentially, the overall percentage increase is the weighted average of the increase in boys and the increase in girls. The numbers are already expressed as percentages, so we don't need to figure the actual numbers. We can just use the percentages.

Since the original numbers of boys and girls were the same, each percentage is weighted the same when computing the weighted average.