Answer:
[tex] \boxed{\sf Number \ of \ girls \ in \ classroom =15} [/tex]
Given:
Ratio of numbers of girls to boys = 5:4
Total number of students = 27
To Find:
Numbers of girls in classroom
Step-by-step explanation:
Let number of girls be 'x' and number of boys be 'y'
[tex]\sf \implies \frac{x}{y} = \frac{5}{4} \ \ \ \ \ \ \ \ \ \ .....Eq_{1} \\ \\ \sf \implies x + y = 27 \ \ \ \ \ \ \ \ \ \ .....Eq_{2}[/tex]
[tex]\sf \bold{ \large From \ Eq_{1} :} \\ \sf \implies \frac{x}{y} = \frac{5}{4} \\ \\ \sf Taking \: the \: reciprocal \: of \: both \: sides:\\ \sf \implies \frac{y}{x} = \frac{4}{5} \\ \\ \sf Multiply \: both \: sides \: by \: x: \\ \sf \implies y = \frac{4}{5} x[/tex]
[tex]\sf \bold{ \large Substituting \ value \ of \ y \ in \ Eq_{2},} \\ \bold{ \large we \ get:} \\ \sf \implies x + \frac{4}{5} x = 27 \\ \\ \sf Put \: each \: term \: in \: x + \frac{4}{5} x \: over \: the \: common \\ \sf denominator \: 5: \\ \sf \implies \frac{5x}{5} + \frac{4x}{5} = 27 \\ \\ \sf \frac{5x}{5} + \frac{4x}{5} = \frac{5x + 4x}{5}: \\ \sf \implies \boxed{ \sf \frac{5x + 4x}{5}} = 27 \\ \\ \sf 5x + 4x = 9x : \\ \sf \implies \frac{ \boxed{ \sf 9x}}{5} = 27 \\ \\ \sf Multiply \: both \: sides \: of \: \frac{9x}{5} = 27 \: by \: \frac{5}{9} : \\ \sf \implies \frac{9x}{5} \times \boxed{\frac{5}{9}} = 27 \times \boxed{ \frac{5}{9} } \\ \\ \sf \frac{ \cancel{9} \times \cancel{5}}{ \cancel{5} \times \cancel{9}} x = x : \\ \sf \implies \boxed{x} = 27 \times \frac{5}{9} \\ \\ \sf 3 \times \cancel{9} \times \frac{5}{ \cancel{9}} = 5 \times 3 : \\ \sf \implies x = \boxed{5 \times 3} \\ \\ \sf 5 \times 3 = 15 : \\ \sf \implies x = 15[/tex]
So,
Numbers of girls in classroom = 15
