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 middle school students to high school students was 1:8 This year the ratio is 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.
twice as many ms , so there were 9 last year
that means 9 fewer hs this year
To find the number of high school students in the band this year, we need to determine the total number of students in the band this year.
Given that the ratio of middle school students to high school students this year is 2:7, we can find the total number of students as follows:
Let's assume the total number of students in the band this year is x.
According to the ratio, the number of middle school students is 2/9 (2 out of 2+7) times x, which is equal to 18.
So, (2/9)x = 18.
To isolate x, we can multiply both sides of the equation by 9/2:
x = 18 * (9/2).
x = 81.
Therefore, the total number of students in the band this year is 81.
Now, to find the number of high school students in the band this year, we can subtract the number of middle school students from the total number of students:
Number of high school students = Total number of students - Number of middle school students.
Number of high school students = 81 - 18.
Number of high school students = 63.
Since last year the ratio of middle school students to high school students was 1:8, we can determine the number of high school students last year as follows:
Number of high school students last year = 8 * Number of middle school students last year.
Number of high school students last year = 8 * 18.
Number of high school students last year = 144.
The difference in the number of high school students between this year and last year is:
Difference = Number of high school students last year - Number of high school students this year.
Difference = 144 - 63.
Difference = 81.
Therefore, there are 81 fewer high school students in the band this year compared to last year.
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 based on the given information.
Let's assume the number of middle school students last year was x. Since the ratio of middle school students to high school students was 1:8, the number of high school students last year can be calculated as 8x.
This year, the ratio has changed to 2:7. They mention that there are 18 middle school students in the band this year. By setting up a proportion, we can find the number of high school students this year.
(18 middle school students) / (x high school students) = (2 middle school students) / (7 high school students)
Cross-multiplying the proportion:
18 * 7 = 2 * x
126 = 2x
Now we can solve for x:
x = 126 / 2 = 63
Therefore, last year there were 63 middle school students and 8 * 63 = 504 high school students.
To find how many fewer high school students are in the band this year, we subtract the number of high school students this year from last year's number:
504 - (2 * 18) = 504 - 36 = 468 high school students.
So, there are 468 fewer high school students in the band this year.