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

Question

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

Answer 1

This year:

number of middle schoolers --- 2x
number of high schoolers ----- 7x
but 2x = 18
x = 9
So this year there are 18 middle schoolers, and 63 high schoolers. Total = 81

Since all we know from the previous year is the ratio of 1:8 , and there were more last year:

possible cases would be
middle - high - total
10 80 90
11 88 99
12 96 108
etc

Answer 2

To find the number of high school students in the band this year, we need to determine the ratio of middle school students to high school students and use that ratio along with the given number of middle school students.

Given that the ratio of middle school students to high school students this year is 2:7, and there are 18 middle school students, we can set up a proportion to find the number of high school students:

2/7 = 18/x

To solve for x, we can cross-multiply:

2x = 7 * 18

Now, we can solve for x by dividing both sides of the equation by 2:

x = (7 * 18) / 2

x = 63

Therefore, there are 63 high school students in the band this year.

To compare the number of high school students in the band this year to last year, we need to find the number of high school students from the previous ratio.

The ratio of middle school students to high school students last year was 1:8, and we know there were 18 middle school students. To find the number of high school students last year, we can set up a proportion:

1/8 = 18/y

Cross-multiplying:

y = 8 * 18

y = 144

Therefore, there were 144 high school students in the band last year.

To find how many fewer high school students are in the band this year compared to last year, we can subtract the number of high school students this year from the number of high school students last year:

144 - 63 = 81

So, there are 81 fewer high school students in the band this year compared to last year.