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Weight-loss Program Poser (Posted on 2023-06-28) Difficulty: 3 of 5
  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.

See The Solution Submitted by K Sengupta    
Rating: 5.0000 (1 votes)

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Solution computer solution | Comment 2 of 3 |
Well, 8 equations in 8 unknowns is daunting, so the indefatigable computer was programed:

syms s1 s2 a1 a2 p1 p2 j1 j2

eq2=s1==j1+s1+p1+a1-j2-s2-p2-a2 ;
eq3=j1==2*p2;
eq4=s1+p1+a1==4*p2;
eq5=s1+j1==3*s2;
eq6=p1-p2==a1-a2 ;
eq7=2*(s1-s2)==3*(a1-a2);
eq8=s1-s2==p1-p2+20;
eq9=j1+s1-j2-s2==140;

s=solve(eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,s1,s2,p1,p2,...
  a1,a2,j1,j2)
  
and it gave back:

>> weightLossProgram
s = 
  struct with fields:
    s1: 220
    s2: 160
    p1: 170
    p2: 130
    a1: 130
    a2: 90
    j1: 260
    j2: 180
>> 

Each initial with a 1 is that person's weight before the weight-loss program nad those with 2 refer to after weight loss.

  Posted by Charlie on 2023-06-28 16:41:37
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