1. Judy, Scarlett, Phoebe, and Amanda all went through a weight loss diet program.
2. Their combined weight loss after the program was equal to Scarlett's weight before the program.
3. Judy's weight before the program was twice Phoebe's weight after the program.
4. The combined weight of Scarlett, Phoebe and Amanda before the program was four times Phoebe's weight after the program.
5. The combined weight of Judy and Scarlett before the program was thrice Scarlett's weight after the program.
6. Phoebe and Amanda both lost the same amount of pounds.
7. Twice Scarlett's weight loss was equal to thrice Amanda's weight loss.
8. Scarlett lost 20 pounds more than Phoebe.
9. The combined weight loss of Judy and Scarlett is equal to 140 pounds.

Determine the weights of Judy, Scarlett, Phoebe, and Amanda before and after the weight-loss program.

Consider clues 6-8
6)  p = a
7) 2s = 3a
8) s = p + 20
   then 1.5a = a + 20
    a = 40
    
   So A and P lost 40 lbs, and S lost 60
   
From clue 9, J lost 80 lbs

From Clue 2, Scarlet before weighed 40+40+60+80 = 220 lbs
             So Scarlet weighed 160 afterwards
             
From clue 5, Judy before weighed 3*160 - 220 = 260 lbs
             So Judy weighed 180 afterwards
             
From Clue 3, Pheobe after = 260 / 2 = 130
             So Pheobe weighed 170 before
             
From Clue 4, Amanda before = 4*130 - 220 - 170 = 130
             So Amanda weighted 90 pounds after
             
Final Answer:
Judy       260 - 80 = 180
Scarlett   220 - 60 = 160
Pheobe     170 - 40 = 130
Amanda     130 - 40 =  90