Question

at a school number of boys : number of girls = 11:9
there are 124 more boys than girls
work out the total number of students

Answer 1

Please see the attachment

Answer 2

The total number of students is 1240

Step-by-step explanation:

Let the number of boys be x and that of girl be y.

It is given that numbers of boys:number of girls =11:9

Using ratio and proportion property.

$\frac{x}{y} =\frac{11}{9} \\\\\Rightarrow x=\frac{11y}{9}---(i)$

It is also given that there are 124 more boys than girl.

Thus x= 124+y---(ii)

Equating equation (i) and (ii)

$124+y=\frac{11y}{9}$

Cross Multiply

$\Rightarrow 9(124+y)=11y\\\\\Rightarrow 1116+9y=11y$

Bring the like terms together

$\Rightarrow 1116+9y-11y=0\\\\\Rightarrow 1116-2y=0$

Isolate y by subtracting 1116 from both sides.

$\Rightarrow 1116-1116-2y=-1116\\\\\Rightarrow -2y=-1116$

Now divide -2 from both sides

$\Rightarrow \frac{-2y}{-2}=\frac{-1116}{-2} \\\\\Rightarrow y=558$

Substituting the value of y in equation (i)

$x=\frac{11y}{9} \\\\\Rightarrow x=\frac{11\times 558}{9}\\ \\\Rightarrow x=\frac{6138}{9} \\\\\Rightarrow x=682$

So, total number of students = x+y=682+558=1240

Learn More:

60 % of the total students are boys and total number of girls are 320 .find the total number of students and the number of boys.

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