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 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.
The ratio of boys to girls in a marching band is 4:5
Write ratio in two other ways
To find the number of girls who joined the band during the school year, we need to determine the initial number of girls, as well as the final number of girls. Here's how we can calculate it:
1. Determine the initial number of girls:
- The ratio of girls to boys in the band at the beginning of the year is 5 to 7.
- We can set up a proportion to find the initial number of girls: (5/12) = (x/72), where x represents the initial number of girls.
- Cross-multiplying, we have: 5 * 72 = 12 * x.
- Simplifying, we find that the initial number of girls is x = 30.
2. Determine the final number of girls:
- At the end of the year, the ratio of girls to boys was 3 to 4.
- We can set up another proportion to find the final number of girls: (3/7) = (x/48), where x represents the final number of girls.
- Cross-multiplying, we have: 3 * 48 = 7 * x.
- Simplifying, we find that the final number of girls is x = 21.
To find the number of girls who joined the band during the year, we subtract the initial number of girls from the final number of girls: 21 - 30 = -9.
It appears that the result is negative, indicating that there was a decrease in the number of girls during the year. However, it's worth noting that in real-world scenarios, the information provided might not be accurate or complete.