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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?

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  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

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