# The ratio of boys to girls in a certain classroom was 2:3. if boys represented …

The ratio of boys to girls in a certain classroom was $2:3$. If boys represented five more than one third of the class, how many people were there in the class room?

For now, we don't know how many boys and girls there are, so let's just say there are '$b$' boys and there are '$g$' girls.

Now, the ratio of boys to girls tells us that for every $2$ boys, there are $3$ girls. How can we write this algebraically? Well, if $b$ was $2\cdot k$ for some number $k$, then $g$ would be $3\cdot k$ so we get $b=2k$ and $g=3k$. Putting these two equations together we get $\dfrac{b}{2}=\dfrac{g}{3}$ which we can re-write as $3b=2g$.

What can we tell from the other information in the question: boys represented five more than one third of the class.

"Well, a third of the class is $\dfrac{b+g}{3}$ because $b+g$ is the total number of people in the class. So if boys represent five more than this, then $b=5+\dfrac{b+g}{3}$. We can re-arrange this as well to get $g=2b-15$. So, we have two equations

1. $3b=2g$

2. $g=2b-15$

I'll let you solve these simultaneous equations. (Remember to always do a sanity check: if the answers you get aren't whole numbers then something's gone wrong - maybe a boy lost a leg or two - so remember to plug in the answer at the end back in to the information you've been given to make sure it satisfies what you've been told.)

let 'x' total number of boys and girls, 'b' boys 'g' girls for ratio b:g, i.e 2:3

number of boys (b/(b+g))*x ------- 1 number of girls (g/(b+g))*x ------ 2

from the second condition number of boys 1/3*x + 5 -------3

Eque 1 & 3 should be equal, so

(b/(b+g))*x = 1/3*x + 5,

solve it u will get total boys and girls b+g= x = 75,

now counter check the answers all are correct....