If
![\frac{9}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B12%7D%20)
of students were juniors and seniors that leaves the 36 sophomores to be
![\frac{3}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B12%7D%20)
or
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
of attendees. I got
![\frac{9}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B9%7D%7B12%7D%20)
by converting
![\frac{1}{3} to \frac{4}{12} by multiplying it by 4](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B3%7D%20to%20%5Cfrac%7B4%7D%7B12%7D%20by%20multiplying%20it%20by%204)
and adding it to
![\frac{5}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B12%7D%20)
.
Now if 36 is
![\frac{3}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B12%7D%20)
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}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B12%7D%20)
to figure out how many
![\frac{1}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B12%7D%20)
is.
The equation would look like this 36*(3/12)
start with 3/12. this equals .25 or
![\frac{1}{4}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20)
.
Now multiply 36 by .25. this equals 9.
We have 9 students per
![\frac{1}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B12%7D%20)
of the attendees.
To get the amount of seniors add 9 to 36
![\frac{4}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B12%7D%20)
because we already stated
![\frac{3}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B12%7D%20)
is 36.
36+9=45
Now to find the juniors add another 9 to create
![\frac{5}{12}](https://tex.z-dn.net/?f=%20%5Cfrac%7B5%7D%7B12%7D%20)
.
45+9=54
In total you have:
36 sophomores
54 juniors
45 seniors<span />