The ratio of girls to boys in the junior high band is 5 to 7. At the beginning of the year, there were 72 students in band. By the end of the year the ratio of girls to boys was 3 to 4. If there are now 48 boys in the band how many girls joined the band during the school year?

beginning ratio 5:7
Girls=30
Boys=42

ending ration 3:4
Boys=48

48/4=12
12*3=36

Girls=6

36-30=6

6 more girls joined

The ratio of boys to girls in a marching band is 4:5
Write ratio in two other ways

The ratio of girls to boys is 5:7 and there are 72 students at the beginning of the year, so you solve the first part of the problem by saying:
5x + 7x=72
12x=72
x=6
You plug 5(6)=30 girls and 7(6)=42 boys at the beginning of the year.

For the second part of the problem, at the end of the year, the ratio is 3:4 girls to boys and there are 48 boys, how many girls joined the band during the school year?
3/4 = x/48
144=4x
x=36 girls

Answer: So 36 girls at the end of year minus 30 girls at the beginning of the year means that 6 girls joined the band during the school year.