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Neko [114]
3 years ago
6

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

?
Mathematics
1 answer:
Soloha48 [4]3 years ago
6 0

Answer:

\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

Step-by-step explanation:

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

\sf \implies \frac{x}{y} = \frac{5}{4} \ \ \ \ \ \ \ \ \ \ .....Eq_{1} \\ \\ \sf \implies x + y = 27 \ \ \ \ \ \ \ \ \ \ .....Eq_{2}

\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

\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

So,

Numbers of girls in classroom = 15

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