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I need to understand how to do this math problem and how to explain how one can do the problem.

Rollie was successful in losing weight. He had a set 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 the three months he was just three pounds over his ideal weight. How many pounds did he lose in those three months?

Explain how you come up with your solution.

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1 Answer

Let W be Rollie's initial weight, and let G stand for the "goal" weight.

Weight at beginning of first month: W

Weight lost during the first month: (1/3)(W - G) + 3

Weight at end of the first month: W - [(1/3)W - (1/3)G + 3] which you can simplify to:

(2/3)W + (1/3)G - 3 which again, is the weight at the end of the first month. Carry out similar steps for the second and third months. There's a lot of algebra, arithmetic, and fractions, so to minimize errors if you're doing this by hand (rather than with a calculator/computer which handles the algebra) I suggest you write each step separately:

Weight at beginning of second month (which is the same as weight at the end of the first month); How much weight is lost during the second month, remembering to take the "(1/3) of the difference" and simplify and then to add 3 pounds more; and weight at the end of the second month, remembering you're now subtracting. Similarly for the third month. You'll get an expression with W's and G's and fractions with 27 in the denominator.

But you also know another name for Rollie's weight at the end of three months: it is G+3, that is 3 pounds over the idea (or goal) weight. So you can set those two expressions equal. Great. Now you have one equation with two unknowns (unless in my haste I made an arithmetic mistake; I got "(8/27)W + (19/27)G - (19/3) = G+3"). So if the starting weight isn't given and the end weight isn't given, you need some other equation to be the second equation.

I would have re-checked my work before posting here but a quick search suggests this weight problem is from a pdf by the Noyce Foundation, and same PDF speaks about "In level E, students are asked to find the exact theoretical chance knowing three conditional probable events expressed as..." which makes me wonder, for two reasons, whether this document has some mathematical typos if not errors. Because one speaks of "conditional probabilities" not "conditional probable events" and secondly, because that other problem, E, does not give conditional probabilities, like "the probability of being male given you were born in North America" would be a conditional probability. But it gives just "the probability of..male" and other non-conditional probabilities. So there are some definite typos (misprints) if not outright errors in problem E...so I wonder if the same is true for problem D, the weight problem.

Maybe they mean for the teacher to make up a problem in which W or G is known, and otherwise following the pattern of the problem in question? Their suggesting "guess-and-check" as a method sounds like it's one of those problems ("He started at 200 pounds. He lost 1/3 of the difference to...plus an additional 3 pounds") they might have in mind. Please post here if you have update or clarification.

Comments

I just wonder why you can't solve this problem. Well, the answer is 28.5 lb.
This is a kind of tedious problem but the answer is very clear. We usually think if there are two variables, we need 2 equations to solve. 
Yes, it is right. Now we have only one equation in this problem. but the problem didn't ask us "W" and "G". If the problem asked us "G" and "W" , we can't solve them . But it only asked us "the weight he loses". 
 
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
 
Now we have one more clue ; I copied and  pasted your explanation below.
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"But you also know another name for Rollie's weight at the end of three months: it is G+3, that is 3 pounds over the idea (or goal) weight. So you can set those two expressions equal. Great. Now you have one equation with two unknowns (unless in my haste I made an arithmetic mistake; I got "(8/27)W + (19/27)G - (19/3) = G+3
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Your explanation is right but the calculation is wrong.
The equation we can get from this explanation is  (8/27)(W-G)=28/3
At this equation, we can get the value of " W-G"
W-G = 63/2.
 
Now we go back to the question. How many pounds he lose in  in 3 month?
Just pluged in the "W-G" value .
 
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
 
The first month he lost 13.5 lb, second month 9 lbs, third month 6 lbs. The total is 28.5 lbs
This is my first time to post here, I tried to edit the comment but I couldn't find the way. So I posted the comment again. Sorry for this. Your calculation is right . I didn't see (-19/3) part at your explanation.
Your calculation is right. But you needed to do more steps to solve the question.
 
The most important clue  of this question is catching a common factor( W-G). 

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