# If the ratio of girls to boys is 2:3 and there are 42 boys .find the number of girls and total number of students? This sum is of ratio and proportion.

Jun 23, 2018

There are $70$ students in total, of which $28$ are girls.

#### Explanation:

We begin by setting up an algebraic relationship to model the ratio of girls to boys, with

• $g =$ the number of boys
• $b =$ the number of girls:

So

$\frac{1}{2} \cdot g = \frac{1}{3} \cdot b$

As we know the number of boys, we can plug in that value:

$\frac{1}{2} \cdot g =$1/3 * 42#

This relationship simplifies to

$\frac{1}{2} \cdot g = 14$

which in turn simplifies to

$g = 14 \cdot 2 = 28$

Then, to determine the total number of students, we can simply total the number of girls + the number of boys:

$28 + 42 = 70$

Therefore, there are $70$ total students, of which $28$ are girls and $42$ are boys.