Lisa charger $25 per person for private tutoring and $18 per person for a group tutoring session. One day in January, Lisa earned $265 from 12 students. How many students of each type did Lisa tutor? Define variables too, please!

You don't have to do the whole problem, I just need to be walked through the steps because I'm confused.

first of all 25x+18y=265
since 265 finishes in 5, and we have $25 and $18 students, it means that $18 students have to be either 5, 10, 15, etc.
try plug in 5 and see.
so if we plug 5 students for $18 we have 25x+18(5)=265
25x=265-90
25x=175
x = 7

so, final answer is 25(7)+18(5)=265
so you have 7 students at $25
and 5 students at $18