Answer:
35
Step-by-step explanation:
At the beginning, the ratio number of girls : number of boys is
[tex]\frac{G}{B}=\frac{3}{2}[/tex] (1)
where
G is the number of girls
B is the number of boys
Later, seven more girls join the class, and two boys drop the class, so the new numbers of girls and boys are
[tex]G'=G+7[/tex]
and
[tex]B'=B-2[/tex]
We are also told that now the ratio is
[tex]\frac{G'}{B'}=\frac{5}{2}[/tex]
Substituting the two equations above,
[tex]\frac{G+7}{B-2}=\frac{5}{2}[/tex] (2)
Also, from eq.(1) we can write
[tex]G=\frac{3}{2}B[/tex]
And substituting into (2) and re-arranging, we can find B:
[tex]\frac{\frac{3}{2}B+7}{B-2}=\frac{5}{2}\\\frac{3}{2}B+7=\frac{5}{2}(B-2)=\frac{5}{2}B-5\\B=12[/tex]
And so
[tex]G=\frac{3}{2}B=\frac{3}{2}(12)=18[/tex]
Therefore, the total number of students in the class BEFORE is
[tex]N=G+B=18+12=30[/tex]
And so, after we have:
[tex]G'=G+7=18+7=25\\B'=B-2=12-2=10[/tex]
So the new number of students is
[tex]N'=G'+B'=25+10=35[/tex]
