Question

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

A. 21
B. 35
C. 40
D. 42
E. 56

Answer 1

The number of high school students in the band this year compared to last year is 81 fewer.

Explanation:

To solve this problem, we can use the concept of ratios and proportions.

First, let's calculate the number of high school students in the band this year.

If 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 the proportion:

2 / 7 = 18 / x

Where x represents the number of high school students this year.

Solving for x:

x = (7 * 18) / 2

x = 63

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

Next, let's calculate the number of high school students in the band last year.

If the ratio of middle school students to high school students last year was 1:8, we can set up the proportion:

1 / 8 = y / 18

Where y represents the number of high school students last year.

Solving for y:

y = (8 * 18) / 1

y = 144

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

Finally, we can determine the difference in the number of high school students between this year and last year:

Difference = Number of high school students last year - Number of high school students this year

Difference = 144 - 63

Difference = 81

Therefore, the number of high school students in the band this year compared to last year is 81 fewer.