Total students = 48
Ratio of boys to girls = 5:3
A ratio of 5:3 means for every 5 boys, there are 3 girls.
Boys = 5 parts
Girls = 3 parts
Total parts = 5 + 3 = 8 parts
Since total students = 48:
8 parts = 48 students
1 part = 48 ÷ 8 = 6 students
Therefore:
Boys = 5 × 6 = 30
Girls = 3 × 6 = 18
The new ratio needs to be 6:5 (boys to girls).
The number of boys stays the same = 30
Let x be the number of girls to add.
New number of girls = 18 + x
Number of boys = 30
The new ratio is:
30:(18+x)=6:5
18+x30=56
30×5=6×(18+x)
150=108+6x
42=6x
x=7
Therefore, 7 girls need to be added to the gathering.