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?
I do not seem to get how to solve it. Can somebody please help? 
 A: 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


*

*$3b=2g$

*$g=2b-15$
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.)
A: 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....
A: B:G
2:3
Suppose $2x$ is the number of boys and $3x$ is number of girls.
2x:3x
Total number of students in classroom = 2x+3x = 5x
According to condition,
Boys = 1/3 of the class students + 5
Put values here
$$2x = (1/3 * 5x ) + 5$$
x = 15
Question is how many people were there in the class means total number of student that is 5x
5x = 5(15) = 75
