Respuesta :
Answer: The ratio of boys to girls would be 3 : 5 .
Step-by-step explanation:
Since we have given that
Number of boys and girls = 32
Fraction of boys are going on a field trip = [tex]\dfrac{2}{3}[/tex]
Fraction of girls are going on a field trip = [tex]\dfrac{3}{4}[/tex]
Number of children left = 9
Let the number of boys be 'b'.
Let the number of girls be 'g'.
According to question, it becomes ,
[tex]b+g=32------------(1)\\\\32-9=\dfrac{2}{3}b+\dfrac{3}{4}g\\\\23=\dfrac{2b}{3}+\dfrac{3g}{4}-------------(2)[/tex]
From eq(1), we get that g = 32-b
So, it becomes,
[tex]\dfrac{2}{3}b+\dfrac{3}{4}(32-b)=23\\\\\dfrac{2}{3}b+24-\dfrac{3}{4}b=23\\\\\dfrac{2}{3}b-\dfrac{3}{4}b=23-24=-1\\\\\dfrac{8b-9b}{12}=-1\\\\\dfrac{-b}{12}=-1\\\\b=-1\times -12\\\\b=12[/tex]
so, number of girls would be 32 - b = 32 - 12 = 20
So, Ratio of boys to girls in class would be 12 : 20 = 3 : 5.
Therefore, the ratio of boys to girls would be 3 : 5 .
