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Solution to Puzzle 143.  WEIGHT LOSS PROGRAM

Jenny, Sally, Peggy, and Alice all went through a weight loss diet program.  Their combined weight loss after the program was equal to Sally's weight before the program.  Jenny weight before the program was twice Peggy's weight after the program.  The combined weight of Sally, Peggy and Alice before the program was four times Peggy's weight after the program.  The combined weight of Jenny and Sally before the program was thrice Sally's weight after the program. Peggy and Alice both loss the same amount of pounds.

Twice Sally's weight loss was equal to thrice Alice weight loss.  Sally loss 20 pounds more than Peggy.  The combined weight loss of Jenny and Sally is equal to 140 pounds.

What are the weights of Jenny, Sally, Peggy, and Alice before and after the weight loss program?

Solution:

Let j,s,p,a be Jenny's, Sally's Peggy's and Alice's weights after program.

Let J,S,P,A be be Jenny's, Sally's Peggy's and Alice's weights before program.

J+S+P+A-j-s-p-a = S

J= 2*p

S+P+A=4*p

J+S=3*s

P-p=A-a

2*(S-s)=3*(A-a)

S-s=P-p+20

J-j-S-s=140

Solving the eight equations yields:

J=260;S=220;P=170;A=130;

j=180;s=160;p=130;a=90

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The Universe in a Handkerchief: Lewis Carroll's Mathematical Recreations, Games, Puzzles, and Word Plays

Author:  Martin Gardner 

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