Question

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 classroom?

Answer 1

Well, if you let the number of boys = B and the number of girls = G, then you can use the given information to write a couple of different equations here.

From the ratio you have:
\[\Large \dfrac{ B }{ G }=\dfrac{ 2 }{ 3 }\]which you can solve for B, by multiplying both sides by G.

And then you also have that "boys represented five more than one third of the class" How can you write that as an algebraic expression using B and G?

Start with an expression for the WHOLE class: B + G
Now you need 1/3 of THAT.
And then you need to add 5 to THAT. Can you come up with that expression?

Answer 2

Well, once you get that expression, you can use the FIRST expression, solved for B, and substitute it into the 2nd expression for the B's. then solve for G. That gives you the number of girls; then use the first expression to get B, then add to get the total number in the class.

Answer 3

confusing

Answer 4

The ratio of boys to students in the class is:
\[\dfrac{b}{c} = \frac{2}{5}\]
\[b = \dfrac{1}{3}c + 5\]

So:
\[\dfrac{\dfrac{c}{3} + 5}{c} = \frac{2}{5}\]

Now solve for c:
\[5\left(\frac{c}{3} + 5\right) = 2c\]
\[\frac{5c}{3} + 25 = 2c\]
\[25 = 2c - \frac{5}{3}\]
\[25 = \left(2 - \frac{5}{3}\right)c\]
\[25 = \left(\frac{6}{3} - \frac{5}{3}\right)c\]
\[25 = \frac{1}{3}c\]
\[25 = \frac{c}{3}\]
\[75 = c\]

Answer 5

given condition is b:g=2:3
now strength of total class would be (b+g)
in given statement of the question "boys represent five more than one third of the class meaning "
b=1/3(b+g)+5
now u have the two equations solve then

Answer 6

@bilbobaggins , they wanted the total number of students in the whole class, not justbthe number of boys.