Search 83,317 tutors
FIND TUTORS
Ask a question
0 0

Losing Weight Challenge

1. Reuben was successful in losing weight. He had a goal weight in mind. He went on a diet for three months. Each month, he would lose one-third of the difference between his current weight and his goal weight and an additional three pounds. At the end of three months, he was just 3 pounds over his goal weight. How many pounds did he lose in those three months?
Tutors, please sign in to answer this question.

1 Answer

Let Wk=weight after month k, and W0=starting weight, G = goal weight
Wk+1=Wk-1/3(Wk-G)=(2/3)Wk+(1/3)G
W1=(2/3)W0+(1/3)G
W2=(2/3)W1+(1/3)G=(2/3)((2/3)W0+(1/3)G)+(1/3)G=(4/9)W0+(5/9)G
W3=(2/3)W2+(1/3)G=(2/3)((4/9)W0+(5/9)G)+(1/3)G=(8/27)W0+(19/27)G
(8/27)W0+(19/27)G=G+3
(8/27)W0=(8/27)G+3
W0=G+81/8
Weight lost was 3 pounds short of goal.  81/8=10 1/8 He lost 7 1/8 pounds.