Answer:Rod installed  7 screen doors
Step-by-step explanation:
 Step 1
 Let the number of screen door = x
 And the number of wooden doors = y
 since he installed 18 doors , we have that 
 screen door + wooden doors = 18
x + y = 18------ equation 1
 Also the cost to install a screen  door -= $85
 and to install a wooden door = $115
 And he was therefore paid a total of $1850
 Therefore 
 85x + 115 y = $1860------- equation 2
Step 2----- Solving 
x + y = 18------ equation 1
85x + 115 y = $1860------- equation 2
 Multiplying equation 1 BY 85
85x + 85y= 1530------- equation 3
85x + 115 y = $1860------- equation 4
subtracting from equation 1 from (2)
115y- 85y= 1860-1530
30y=330
 y = 330/30 = 11
 
 To find x 
 x+ y=18
 x= 18-y
 x= 18-11= 7
 Rod installed  7 screen doors and 11 wooden doors.