Question 803073
This is a system of equations problem, meaning that you need two equations to solve for two variables (number of students, number of faculty).

The situation is $10 x (the number of students) + $25 x (the number of faculty) = $1300 total

If we use variables, we get

{{{10s + 25f = 1300}}}

The other equation we need is a bit simpler but a little more hidden in the question:

There are only two types of people (students, faculty) attending and we know the total is 100, so our equation is 

{{{s + f = 100}}}

From here, we can use Elimination or Substitution to solve for the number of students, s.

We'll use substitution:

If we solve 

{{{s + f = 100}}}

for f by subtracting s from both sides, we get

{{{f = 100 - s}}}

Now we can plug f back into the other equation and solve for s:

{{{10s + 25(100 - s) = 1300}}}
{{{10s + 2500 - 25s = 1300}}}  ;  Distribute 25
{{{-15s + 2500 = 1300}}}          ;  Combine "like" terms
{{{-15s = -1200}}}                    ;  Subtract 2500 from both sides
{{{s = 80}}}                                ;  Divide both sides by -15

So we find out that there are 80 students. 

You can check your answers by realizing that since there are 80 students out of 100, the other 20 must be faculty. 

Plug s = 80 and f = 20 into your original equation of

{{{10s + 25f = 1300}}}

to get

{{{10(80) + 25(20)}}}
={{{800 + 500)}}}
={{{1300}}}

And it checks out.