Question

The ratio of boys to girls in the 9th grade is 7 to 8. There are 304 girls. How many boys are there?

Answer 1

Given:

The ratio of boys and girls in 9th grade is 7:8

The number of girls in the 9th grade is 304.

To find:

The number of boys in the 9th grade

So,

Let the number of boys be 7x

And let the number of girls be 8x

Now,

As given in the question

The number of girls in 9th grade is = 304

⇒ 8x = 304

⇒ x = 304/8

[By transporting 8 to RHS]

⇒ x = 38

∴ the value of x is 8

Now,

The number of boys in 9th grade is

= 7x

= 7*38

= 266

Hence,

There are 266 boys in the 9th grade.

- - -

Verification:

The number of girls = 304

And the number of boys = 266

Now,

Their ratio

= boys/girls

= 266/304

[Dividing both numerator and denominator by 38]

= 7/8

Thus,

The ratio of boys to girl

= 7:8

Hence, verified

Answer 2

Given :

• Ratio of boys to girls = 7:8
• Number of girls = 304.

To find:

• The number of boys.

Solution :-

Suppose the number of boys and number of girls be 7x and 8x.

But , number of girls =304

$\therefore{ \sf{8x = 304}}$

Now,

$: \implies{ \sf {8x=304}} \\ \\ : \implies{ \sf { x = \frac {304}{8}}} \\ \\ : \implies{ \boxed{\tt {x=38}}}$

$\underline {\therefore {\bf{The \: number \: of \: boys \: is \:(7 \times 38) = 266.}}}$

Verification :

We have,

• Number of boys = 266
• Number of girls = 304

Ratio of boys to girls :

$: \implies{ \sf {\frac {266}{304}=7:8}} \\ \\ : \implies{ \sf { \frac {7}{8}=7:8}}\\ \\ : \implies{ \sf{ 7:8=7:8}} \\ \\ :\implies{\boxed {\tt{ LHS=RHS}}}$

$\underline{\therefore {\bf{Verified.}}}$