Question

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? Expla

Answer 1

Answer:

Step-by-step explanation:

Last year

Ratio of the number of middle school students to number of high school students = 1 : 8

Total ratio = 9

Middle school = 1

High school = 8

Total students in the band = x

Middle school = 1/9x

High school = 8/9x

Total = 1/9x + 8/9x

This year

Ratio of the number of middle school students to number of high school students = 2 : 7

Total ratio = 9

Middle school = 2

High school = 7

Total students = x

Middle school = 2/9x

High school = 7/9x

Total = 2/9x + 7/9x

If there are 18 middle school students in the band this year

2/9x = 18

x = 18÷2/9

= 18 × 9/2

= 81

x = 81

Last year:

1/9x + 8/9x

= 1/9 * 81 + 8/9 * 81

= 9 + 72

= 81

This year

2/9x + 7/9x

2/9*81 + 7/9*81

= 18 + 63

=81

Change in middle school =this year - last year

= 18 - 9

= 9 (increase)

Change in high school = this year - last year

= 63 - 72

= -9 (decrease)