Question

The ratio of boys to girls in a group is 7:1. If there are 54 more boys than girls, work out how many boys there are.

Answer 1

Step-by-step explanation:

let the no. of girls be X

let the no. of boys be X+54

a/c,

$\frac{x + 54}{x} = \frac{7}{1}$

$7x = x + 54$

$6x = 54$

$x = 9$

so the no. of girls = 9

the no. of boys = 9+54

= 63

Answer 2

Answer:

Hi there! Here is your answer mate!

63 boys are there.

Step-by-step explanation:

Given:

Ratio of boys and girls = 7:1

Boys more than girls (or girls lees than boys) = 54

Asked:

Number of boys = ?

Solution:

Let the number of boys and girls be 'x',

Equation formed:

$\frac{x \ + \ 54}{x} = \frac{7}{1}$

⇒ 7x = x + 54

⇒ 7x - x = 54

⇒ 6x = 54

⇒ x = $\frac{54}{6}$

⇒ x = 9

Number of boys = 7x = 7 × 9 = 63 boys

Hence, there are 63 boys.

Verification:

We will now verify our answer to check that our answer which we just got now is correct or not?

We find out that,

Boys = 63

We knew = Number of Girls is 54 less than Number of boys

Hence, number of girls = 63 - 54 = 9

Number of Girls = 9

Now we will find the ratio between Number of boys and Number of girls. If the ration which we will find now and the ratio which came now is same/equal then our answer is exactly correct!

$\frac{Number \ of \ Boys}{Number \ of \ Girls} = \frac{63}{9}$

⇒ $\frac{63}{9}$ ÷ $\frac{8}{9} = \frac{7}{1}$

Ratio between Number of boys and Number of girls = 7:1

The ratio between Number of boys and Number of girls given in Question and the ratio between Number of boys and Number of girls we just find now is same/equal.

It means our answer is correct!

Hope it helps!