Airline fares for a flight from dallas to austin are $30 for first class and $25 for tourist class. if a flight had 52 passengers who paid a total of $1360, how many first class passengers were on the trip?

Set up 2 equations.(x = number of people in first class, y = tourist class)

30x + 25y = 1360
x + y = 52

You have 2 equations and 2 unknown. You can solve them.
I like to use the substitution method 

Because    y = 52 - x
Then          30x + 25(52 - x) = 1360, solve for x.

30x + 1300 - 25x = 1360
5x = 60
x = 12

Use the x to solve y
30(12) + 25y = 1360
360 + 25y = 1360
25y = 1000
y = 40