The school band is compromised 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? Explain
To solve this problem, we need to find the number of high school students in the band this year and compare it with the number from last year.
Let's say last year the number of middle school students is M and the number of high school students is H.
From the given information, we know that last year's ratio of middle school students to high school students was 1:8. Therefore, we can set up the equation: M/H = 1/8.
This year, the number of middle school students is given as 18, and the ratio of middle school students to high school students is 2:7. Setting up the equation for this year, we have: 18/H = 2/7.
Now we can solve for the value of H for this year. Cross multiplying, we get 18 * 7 = 2 * H. Simplifying, we find that 126 = 2H, so H = 126/2 = 63.
Now we can compare the number of high school students from last year (H) with the number this year (63).
To find the difference, we subtract the number from this year (63) from the number last year (H).
Therefore, the difference in the number of high school students between this year and last year is: H - 63.
This will give us the number of fewer high school students in the band this year compared to last year.