The weight he lost in the first month : 1/3(W-G) + 3 The weight he lost in the second month : 2/9(W-G)+2 The weight he lost in the third month:4/27(W-G)+4/3

Question

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

Answer 1

The weight he lost was 3 pounds short of his targeted loss. Therefore

1/3(W-G) + 3 + 2/9(W-G) + 2 + 4/27(W-G) + 4/3 = (W-G) - 3

                         (9/27 + 6/27 + 4/27)(W-G) + 19/3 = (W-G) - 3

                                              (19/27)(W-G) + 19/3 = (W-G) - 3

                                                                         28/3 = (8/27)(W-G)

                                                                         63/2 = (W-G)

So, his goal was to lose 21.5 pounds.

He fell 3 pounds short, so, he lost 18.5 pounds.