Question

School meeting was attended only by sophomores, juniors, and seniors. 5/12 of those who attended were juniors, and 1/3 were seniors. If 36 sophomore attended, what was the total number of students who attended the meeting ??

Answer 1

If $\frac{9}{12}$ of students were juniors and seniors that leaves the 36 sophomores to be $\frac{3}{12}$ or $\frac{1}{4}$ of attendees. I got $\frac{9}{12}$ by converting $\frac{1}{3} to \frac{4}{12} by multiplying it by 4$ and adding it to $\frac{5}{12}$.

Now if 36 is $\frac{3}{12}$ of the equation that means theirs at least 36 juniors and seniors.

Lets start with seniors. there should be just over 36 of them there. Lets start by multiplying 36 by $\frac{3}{12}$ to figure out how many $\frac{1}{12}$ is.
The equation would look like this 36*(3/12)
start with 3/12. this equals .25 or $\frac{1}{4}$.
Now multiply 36 by .25. this equals 9.

We have 9 students per $\frac{1}{12}$ of the attendees.

To get the amount of seniors add 9 to 36 $\frac{4}{12}$ because we already stated $\frac{3}{12}$ is 36.
36+9=45

Now to find the juniors add another 9 to create $\frac{5}{12}$.
45+9=54

In total you have:
36 sophomores
54 juniors
45 seniors

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