Let's call the rent for one month [tex] r [/tex]. Thus, two months of rent would be [tex] 2r [/tex]. Since they only have to pay the $500 fee once, we can add that to the total as a constant (they aren't paying more for the security deposits based on how long they live there).
Thus, the total they pay the landlord is [tex] 2r + 500 [/tex]. Based on the problem, we can say this is equal to $2800:
[tex] 2r + 500 = 2800 [/tex]
Now, we can solve the equation:
[tex] 2r + 500 = 2800 [/tex]
[tex] 2r = 2300 [/tex]
[tex] r = 1150 [/tex]
The rent for one month is $1,150.
