Middle school and high school students compromise the school band, but it always has the same capacity. Last year, there were 1:8 middle school students for every 1:7 high school students. This year, however, there are 2:7 middle school students for every 1:7 high school students. if there are 18 middle school students in the band this year 9 fewer high school students are in the band this year compared to last year.
Last year, there were 1:8 more middle school students than high school students. 1/9 x + 8/9 x = number of middle school students and number of high school students.
This year, the ratio became 2:7 (2:9 + 7:9 = x) (again)
This year's band includes 18 middle school students.
2/9 x = 18
2x = 9 * 18 → x = 81
Total = 81 in the band
the previous year: 1/9 and 8/9 = 9 and 72
2/9 and 7/9 this year equal 18 and 63.
From there, you may determine the modifications:
Middle school receives a +9 (an increase from 1/9 to 2/9)
-9% for high school (down from 8/9% to 7/9%).
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