Question

The school band is comprised of middle school students and high school students, but it always has the same maximum capacity. Last year the ratio of the number of middle school students to the number of high school students was 1:8. However, this year the ratio of the number of middle school students to the number of high school students changed to 2:7. If there are 18 middle school students in the band this year, how many fewer high school students are in the band this year compared to last year?

Answer 1

> Last year the ratio of the number of middle school students
> to the number of high school students was 1:8.
1/9 x + 8/9 x = makeup of middle and high school students

> this year the ratio ... changed to 2:7
2/9 x + 7/9 x = x (again)

> there are 18 middle school students in the band this year
2/9 x = 18
2x = 9 * 18 → x = 81

Total = 81 in band ...
Last year:
1/9 and 8/9 = 9 and 72
This year
2/9 and 7/9 = 18 and 63

And from there you can figure out the changes:
+9 for middle school (which is increase from 1/9 to 2/9)
--9 for high school (which is decrease from 8/9 to 7/9)