ANSWER
Quotient:

Remainder:

EXPLANATION
The given functions are

and

We want to find the remainder and quotient when f(x) is divided by g(x).
We perform the long division as shown in the attachment.
The quotient is

The remainder is
Ratio is 5girls:7boys with total 72 students
5+7= 12
72➗12= 6
6(5:7)= 30 girls : 42 boys
New ratio is 3:4 with 48 boys
48➗4= 12
So for girls 3x12= 36
So started with 30 girls ended with 36 girls... 6 girls joined band during the school year.