Question

The ratio of girls to boys in Liza’s classroom is 5 to 4. How many girls are in her classroom if there is a total of 27 students?

Answer 1

`\boxed{\sf Number \ of \ girls \ in \ classroom =15}`

Given:

Ratio of numbers of girls to boys = 5:4

Total number of students = 27

To Find:

Numbers of girls in classroom

Explanation:

Let number of girls be 'x' and number of boys be 'y'

`\sf \implies (x)/(y) = (5)/(4) \ \ \ \ \ \ \ \ \ \ .....Eq_(1) \\ \\ \sf \implies x + y = 27 \ \ \ \ \ \ \ \ \ \ .....Eq_(2)`

`\sf \bold{ \large From \ Eq_(1) :} \\ \sf \implies (x)/(y) = (5)/(4) \\ \\ \sf Taking \: the \: reciprocal \: of \: both \: sides:\\ \sf \implies (y)/(x) = (4)/(5) \\ \\ \sf Multiply \: both \: sides \: by \: x: \\ \sf \implies y = (4)/(5) x`

`\sf \bold{ \large Substituting \ value \ of \ y \ in \ Eq_(2),} \\ \bold{ \large we \ get:} \\ \sf \implies x + (4)/(5) x = 27 \\ \\ \sf Put \: each \: term \: in \: x + (4)/(5) x \: over \: the \: common \\ \sf denominator \: 5: \\ \sf \implies (5x)/(5) + (4x)/(5) = 27 \\ \\ \sf (5x)/(5) + (4x)/(5) = (5x + 4x)/(5): \\ \sf \implies \boxed{ \sf (5x + 4x)/(5)} = 27 \\ \\ \sf 5x + 4x = 9x : \\ \sf \implies \frac{ \boxed{ \sf 9x}}{5} = 27 \\ \\ \sf Multiply \: both \: sides \: of \: (9x)/(5) = 27 \: by \: (5)/(9) : \\ \sf \implies (9x)/(5) * \boxed{(5)/(9)} = 27 * \boxed{ (5)/(9) } \\ \\ \sf \frac{ \cancel{9} * \cancel{5}}{ \cancel{5} * \cancel{9}} x = x : \\ \sf \implies \boxed{x} = 27 * (5)/(9) \\ \\ \sf 3 * \cancel{9} * \frac{5}{ \cancel{9}} = 5 * 3 : \\ \sf \implies x = \boxed{5 * 3} \\ \\ \sf 5 * 3 = 15 : \\ \sf \implies x = 15`

So,

Numbers of girls in classroom = 15