Math problem for you guys!!

[janice]

I have a math problem for you guys, or as Tash says--a "maths" problem!  hehe
---------------------------------------------------------------------------------

Dieter 1 says" I lost 1/8 of my weight. I lost 19 pounds."

Dieter 2 says" I lost 1/6 of my weight, and now  you weigh 2 pounds less than I do" How much weight did Dieter 2 lose?"

We know #1 weighs 152 and dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???

[donjuan]

Dieter 2 weighed 184.8 lbs before losing the weight.

let x be dieter 2's weight before losing weight:

x - (x/6) = 154

remove common factor of x -->
x(1-(1/6)) = 154

x = 154 / (1-(1/6))

x = 154/0.833333

x = 184.8

  proof:

184.8 - (184.8/6) = 154?

184.8 - 30.8 = 154 ---> yes, it does

information about dieter one is just superfluous and meant to screw us up.. isnt it, Janice?? The problem would have been much more fun if you didnt say dieter 1 weighed 152 lbs after dieting, but told us dieter 1's starting weight.
donjuan

[janice]

information about dieter one is just superfluous and meant to screw us up.. isnt it, Janice??

Maybe, but maybe not!   
Anybody else?  Or is donjuan correct?

[gorbee natcase]

just stick to the diet you will be fine

[xvimbi]

It depends on how you look at it.

Dieter 1 has lost 1/8 (=19 lbs) of his weight. His weight was 8 * 19 = 154, but since he lost 1/8 of it, it is now 133 lbs (not 154 lbs). Dieter 2 thus weighs 135 lbs, which corresponds to 5/6 of his previous weight (because he lost 1/6). Thus, he lost 135/5 = 27 lbs.

This kind of problems usually has whole numbers as results 

[donjuan]

It depends on how you look at it.

Dieter 1 has lost 1/8 (=19 lbs) of his weight. His weight was 8 * 19 = 154, but since he lost 1/8 of it, it is now 133 lbs (not 154 lbs). Dieter 2 thus weighs 135 lbs, which corresponds to 5/6 of his previous weight (because he lost 1/6). Thus, he lost 135/5 = 27 lbs.

This kind of problems usually has whole numbers as results 

how can that be??
dieter 1's weight was never 154.  Janice told us in the question 154 is the end weight of dieter 2.  (since 152 is 2 less than 154, we have to assume the numbers are refering to the weights afterwards "and now you weigh 2 lbs less than I do")
xvimbi, it sounds like you think the 154 lbs could be the starting or finishing weight depending on how in you look at it.  when I read "dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???
", the only way I can see how it makes sense is if 154 lbs is the end weight -we are given it- and we are asked to find the starting weight, which will be higher.

do I make any sense?

[xvimbi]

how can that be??
dieter 1's weight was never 154.  Janice told us in the question that that number is the end weight of dieter 2.  (since 152 is 2 less than 154, we have to assume the numbers are refering to the weights afterwards "and now you weigh 2 lbs less than I do")
xvimbi, it sounds like you think the 154 lbs could be the starting or finishing weight depending on how in you look at it.  when I read "dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???
", the only way I can see how it makes sense is if 154 lbs is the end weight -we are given it- and we are asked to find the starting weight, which will be higher.

does that make any sense?

Sorry, I made a typo: 8*19=152, not 154. So, my first two statements should read: "Dieter 1 has lost 1/8 (=19 lbs) of his weight. His weight was 8 * 19 = 152, but since he lost 1/8 of it, it is now 133 lbs (not 152 lbs)." The rest is correct.

I think, Janice's last statement was there to confuse, not the first one. It is semantically not entirely clear if the numbers refer to "before" or "after". Initially, I didn't look at Janice's "hint" and arrived at 27 lbs right away, but then I saw your reply and thought "wait a second, perhaps that's the right way to look at it". I was however puzzled by the odd result. When Janice came back with her reply, I thought, perhaps my way of looking at it is the right one. I guess, we will have to wait for her answer.

[Stolzing]

If you say "I lost 1/8th of my weight.", it means from your original weight, not final.  Otherwise it's like saying, "I ate half my pizza" and showing 2/3 a plate of pizza.  It's just wrong semantically to do it that way.  It should be 184.8 unless it's a trick question.  But it's supposed to be a "math problem" not a riddle.

[xvimbi]

If you say "I lost 1/8th of my weight.", it means from your original weight, not final. 

But it does say exactly that. That's why his original weight is 152, but it is now only 133 lbs. That's exactly what it says.

[Stolzing]

Sorry, I misread your argument, disregard that last post.

I agree with donjuan's statement here:

xvimbi, it sounds like you think the 154 lbs could be the starting or finishing weight depending on how in you look at it.  when I read "dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???
", the only way I can see how it makes sense is if 154 lbs is the end weight -we are given it- and we are asked to find the starting weight, which will be higher.

I disagree with this:

" think, Janice's last statement was there to confuse, not the first one. It is semantically not entirely clear if the numbers refer to "before" or "after". "

Since it says "We know #1 weighs 152 and dieter 2 weighs 154".  That indicates it means "after" since it's present tense.

[donjuan]

But it does say exactly that. That's why his original weight is 152, but it is now only 133 lbs. That's exactly what it says.

ay me I see how you see it, but I still think Im right

Xvimbi, if I am understanding you correctly, you are debating whether or not dieter 2 lost 184.8/6 lbs (As I think) or 154/6 lbs.  Well, after both people have finished losing weight, they are 2 lbs apart.  154 and 152 are 2 lbs apart, so hey hey hey these must be the current (thin) weights.  also,

Since it says "We know #1 weighs 152 and dieter 2 weighs 154".  That indicates it means "after" since it's present tense.

ahh, touche' 
well, on Jenny Craig commercials, the thin woman says "I lost 50 lbs!" and she is describing how she looks now to how she did 6 weeks ago, for example.  If I were bragging about how i lost weight, I would definately say "I lost 1/6 of my old weight" rather than say "I lost 1/6 of my current weight."  The latter statement just doesnt make any sense..

Janice, please - what is the answer?? Im starting to second guess myself here  

[xvimbi]

Sorry, I misread your argument, disregard that last post.

I agree with donjuan's statement here:
I disagree with this:Since it says "We know #1 weighs 152 and dieter 2 weighs 154".  That indicates it means "after" since it's present tense.

That's why I said, the problem as posed is semantically (and logically) inconsistent. I assume only the first two statements to be relevant, which will lead to my solution. It could simply be that Janice added the last statement herself, not realizing that it is inconsistent

[donjuan]

oh, another thing, xvimbi:

if 152 and 154 are the originals, then you must agree with this statement:
                  
            2 lb difference in the end
                              |
                              v
(152-(152/8)) + 2 = (154-(154/6))
^^^^^^^^^              ^^^^^^^^^^
{    ||                   }    {       ||              }
{ dieter 1's weight }    {dieter 2's weight }
{ after losing        }     {  after losing      }

Both sides of the equation dont match up,
therefore 154 and 152 must not be the starting (fat) weights

[xvimbi]

oh, another thing, xvimbi:

if 152 and 154 are the originals, then you must agree with this statement:
                  
            2 lb difference in the end
                              |
                              v
(152-(152/8)) + 2 = (154-(154/6))
^^^^^^^^^              ^^^^^^^^^^
{    ||                   }    {       ||              }
{ dieter 1's weight }    {dieter 2's weight }
{ after losing        }     {  after losing      }

Both sides of the equation dont match up,
therefore 154 and 152 must not be the starting (fat) weights

Yes, that's what I'm saying all along: Janice's last statement is incorrect and must be ignored. There is a difference of 2 between the weights after losing weight. Thus, the weights before are 152 for dieter 1 and 162 lbs for dieter 2.

Let's see:

(152-152/8)+2 =? 162-162/6
135 =! 135, QED

In summary:
dieter 1: before = 152; after = 133; lost 19
dieter 2: before = 162; after = 135; lost 27

[donjuan]

janice told us dieter 2 weighs 154 lbs (lets ignore before or after) and it looks like you have ignored this, according to your equation.  Although, if you ignore part of the question (??whats up with that??), then your answer makes sense.

Janice, put an end to this and give the answer!  xvimbi, I know youre very smart so maybe I should just shut up and take my foot out of my mouth, but I still have difficulty seeing it your way.

[xvimbi]

janice told us dieter 2 weighs 154 lbs (lets ignore before or after) and it looks like you have ignored this, according to your equation.  Although, if you ignore part of the question (??whats up with that??), then your answer makes sense.

Janice, put an end to this and give the answer!  xvimbi, I know youre very smart so maybe I should just shut up and take my foot out of my mouth, but I still have difficulty seeing it your way.

As I said earlier, I was perfectly fine with your solution, but I did realize that it does not fulfill all the statements in Janice's post. Neither does mine. Something's gotta give. That's why I said "It depends on how you look at it". Either her last statement is correct and relevant, in which case your solution is the correct one, or it is not correct nor relevant, in which case the other solution is the correct one. It all depends on Janice. I'm convinced she did this to get us all pumped up

[janice]

It all depends on Janice. I'm convinced she did this to get us all pumped up

It is sooooo entertaining to just sit back and watch you guys argue over this!!!  No, I do not know the correct answer, I just saw it somewhere and knew that you guys would have a heyday with it!!  And I was right!

[donjuan]

Either her last statement is correct and relevant, in which case your solution is the correct one, or it is not correct nor relevant, in which case the other solution is the correct one.

Are you saying you like to ignore parts of the question?  You need the question to find a solution.  cmon, use what's there!  You need to use whats given to you, confusing or not! You cant get a plausible answer from your brilliant scheme of not using the question!  im RIGHT!! 


.... j/k

[Stolzing]

As I said earlier, I was perfectly fine with your solution, but I did realize that it does not fulfill all the statements in Janice's post.

Which statement isn't fulfilled in donjuan's solution?

How can you read this:
"We know #1 weighs 152 and dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???"

and think that 154 is referring to the original weight and not the current weight?  Why would it say the original weight and then in the next sentence ask what the original weight was, when it was just stated in the previous sentence?  And why would it say it in the present tense ("weighs 154") instead of past tense ("weighed 154") if it was referring to the old weight?


And for some reason I keep reading "dieter" as pronounced "deeter".

[Dazzer]

here's my take

pardon me i didn't bother to read all the different attempts


D1O - Dieter 1's original weight
D1R - Dieter 1's Reduced weight
D1L - Dieter 1's Loss Weight
similar for 2

Dieter 1 says" I lost 1/8 of my weight. I lost 19 pounds."

hence

Code: [Select]

D1L = 19lbs

 D1O            =            19lbs
------
  8
therefore

Code: [Select]

D1O = 19*8
    = 152lbs
D1R = 152 - 19
    = 133lbs
so Dieter 1 weighs 133lbs NOW, after losing 19lbs from 152lbs ORIGINALLY.

Dieter 2 says" I lost 1/6 of my weight "

Code: [Select]

D2R = D2O * 5/6
, and now  you weigh 2 pounds less than I do" note the use of the word NOW. this means the values we';re concerned with are only those of the present. Meaning -> D1R and D2R.

Code: [Select]

D2R = D1R + 2lbs
    = 133 + 2
    = 135lbs

How much weight did Dieter 2 lose?"

Code: [Select]

D2R = 135lbs
    = D2O * 5/6
D2O = 6/5 * D2R
    = 6/5 * 135
    = 162lbs
D2L = D2O - D2R
    = 162 - 135
    = 27lbs


We know #1 weighs 152 and dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???

Note: this doesn't correlate with the above statement. Which i believe wasn't part of the question, but actually janice's commentary (which is wrong, sorry ). She didn't meant to confuse us. She was just stating the obvious (who couldn't have foudn out that dieter 1 weighed 152 originally?)

So all in all, i'm with Xvimbi.

[xvimbi]

Are you saying you like to ignore parts of the question?  You need the question to find a solution.  cmon, use what's there!  You need to use whats given to you, confusing or not! You cant get a plausible answer from your brilliant scheme of not using the question!  im RIGHT!! 

I worked from the top down. When I came across Janice's last statement, I thought "that doesn't make sense", so I neglected it. You were saying one could neglect the first statement, which I on the other hand believe is vital.

BTW: Dazzer is right (and he used the exact same logic as I did).

Janice: that's pretty lame that you don't know the correct answer. At least tell us which statements belong to the original problem, and whether you (or somebody else) added the last statement. I can't sleep

[donjuan]

from dazzer:

D1L = 19lbs

D1O            =            19lbs
------
  8
therefore


D1O = 19*8
    = 152lbs
D1R = 152 - 19
    = 133lbs

ok, this part makes me see it xvimbis and your way.  It's all because of the D10/8 = 19 lbs that makes 152 lbs the original.  yeah now I get it.  Thank you and sorry for my stubborness
..
.....
........
....................      ....
.....JANICE!!! dont do this to us!!  Understand the question before asking it!

[xvimbi]

from dazzer:
ok, this part makes me see it xvimbis and your way.  It's all because of the D10/8 = 19 lbs that makes 152 lbs the original.  yeah now I get it.  Thank you and sorry for my stubborness
..
.....
........
....................      ....
.....JANICE!!! dont do this to us!!  Understand the question before asking it!

Well, don't be too harsh on yourself. It all depends on how to look at it.

The initial statement was: "I lost 1/8 of my weight. I lost 19 pounds."

One way to look at it is: "I lost 1/8 of my (current) weight. I lost 19 pounds.", which would mean the previous weight was 171 lbs, and the current weight is 152 lbs. There is in fact nothing wrong with this viewpoint.

However, every woman will be able to tell you that that is not the way they look at it. They read the statement like "I lost 1/8 of my (previous) weight. I lost 19 pounds.", thus giving a previous weight of 152 lbs and a current weight of 133 lbs. The same is true for the pizza example above, or for the statement "I lost half of my money", which means "half of the money I had before I made that stupid bet" .

[pianohopper]

OK I have a new one now that you've solved this one:

A man is walking his dog on the lead towards home at a steady 4 mph.  When they are nine miles from home, the man lets the dog off the lead.  The dog immediately runs off towards home at 9 mph.  When the dog reaches the house it turns round and runs back to the man at the same speed.  When it reaches the man it turns back for the house.  This is repeated until the man gets home and lets in the dog.

How many miles does the dog cover from being let off the lead to being let in the house?

(they apparently go for very long walks.  i assume the man is retired.)

[xvimbi]

OK I have a new one now that you've solved this one:

A man is walking his dog on the lead towards home at a steady 4 mph.  When they are nine miles from home, the man lets the dog off the lead.  The dog immediately runs off towards home at 9 mph.  When the dog reaches the house it turns round and runs back to the man at the same speed.  When it reaches the man it turns back for the house.  This is repeated until the man gets home and lets in the dog.

How many miles does the dog cover from being let off the lead to being let in the house?

(they apparently go for very long walks.  i assume the man is retired.)

20.25 mls

[llamaman]

I have a math problem for you guys, or as Tash says--a "maths" problem!  hehe
---------------------------------------------------------------------------------

Dieter 1 says" I lost 1/8 of my weight. I lost 19 pounds."

Dieter 2 says" I lost 1/6 of my weight, and now  you weigh 2 pounds less than I do" How much weight did Dieter 2 lose?"

We know #1 weighs 152 and dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???

A neopets Lenny Conundrum I suppose?

[janice]

Okay, okay, I will put you guys out of your misery!!  I found it amusing that you STILL argued over it even AFTER I stated that I didn't know (or maybe I really do!!! LOL)

The problem with this puzzle is that it is NOT WELL WRITTEN!!  The weight is AFTER dieting, and not the ORIGINAL weight!!  So the answer is 135.

<clap, clap> Donjuan!  It was you who said 135, right?

Gee, that was fun!!!  So let's do another:
(this one is significantly easier)
--My brother and I walk the same route to school every day.  My brother takes 40 minutes to get to school and I take 30 minutes.  Today, my brother left 5 minutes before I did. How long will it take me to catch up with him??

Hey, I think I will do some cooking tonite, so help me out here! 

--I have two recipes which together use a pound of butter.  One recipe takes 1/4 pound more than the other one.  How much butter does each recipe use?

[xvimbi]

OK I have a new one now that you've solved this one:

A man is walking his dog on the lead towards home at a steady 4 mph.  When they are nine miles from home, the man lets the dog off the lead.  The dog immediately runs off towards home at 9 mph.  When the dog reaches the house it turns round and runs back to the man at the same speed.  When it reaches the man it turns back for the house.  This is repeated until the man gets home and lets in the dog.

How many miles does the dog cover from being let off the lead to being let in the house?

In addition to the answer that I already posted, I'd like to offer this little tidbit:

There are several ways to solve this problem. One could calculate at what point the dog and his owner meat the first time, the second time, and so on, until they are both at the house. One quickly realizes that this is a geometric series; one can simply add up the individual terms and arrive at something like 20.2499999 mls. Fair enough.

Of course, it is much easier to use a more pragmatic approach by realizing that the dog runs 2.25 times faster than his owner. So, if it takes his owner (9mls)/(4mls/h)=2.25h to get to the house, the dog will run 2.25h*9mls/h=20.25 mls.

There was a psychologist who wanted to know whether mathematicians and physicists had a preference for one or the other method. He quickly found out that mathematicians used the “geometric series approach“, whereas physicists usually employed the more pragmatic approach. It took the mathematicians a lot longer than the physicists to come up with the solution (something around 30 seconds), because they were adding up, in their head, the geometric series (quite a feat, if you ask me). The physicists took about 4-5 seconds. The psychologist came to John von Neumann, the eminent mathematician and one of the founders of modern computing. Von Neumann came up with the solution in about 3 seconds, the fastest time on record. The psychologist remarked ”Mr. Neumann, you are a mathematician. I would have expected you to use the geometric series method“. Von Neumann replied ”Well, I did!“

[xvimbi]

Okay, okay, I will put you guys out of your misery!!  I found it amusing that you STILL argued over it even AFTER I stated that I didn't know (or maybe I really do!!! LOL)

The problem with this puzzle is that it is NOT WELL WRITTEN!!  The weight is AFTER dieting, and not the ORIGINAL weight!!  So the answer is 135.

<clap, clap> Donjuan!  It was you who said 135, right?

[edited twice]

Janice, I am deeply disappointed, not only have you presented the wrong answer (the question was "what did dieter 2 weigh before losing the weight", not "after losing the weight"), but you also haven't read the replies to your posts carefully (it was Dazzer who presented the correct answer )

[donjuan]

Okay, okay, I will put you guys out of your misery!!  I found it amusing that you STILL argued over it even AFTER I stated that I didn't know (or maybe I really do!!! LOL)

The problem with this puzzle is that it is NOT WELL WRITTEN!!  The weight is AFTER dieting, and not the ORIGINAL weight!!  So the answer is 135.

<clap, clap> Donjuan!  It was you who said 135, right?

Gee, that was fun!!!  So let's do another:
(this one is significantly easier)
--My brother and I walk the same route to school every day.  My brother takes 40 minutes to get to school and I take 30 minutes.  Today, my brother left 5 minutes before I did. How long will it take me to catch up with him??

Hey, I think I will do some cooking tonite, so help me out here! 

--I have two recipes which together use a pound of butter.  One recipe takes 1/4 pound more than the other one.  How much butter does each recipe use?

oh cmon janice, dont go on... blaming the puzzle.. haha"the bad workman blames his tools"
ok, Im gonna do the butter problem (and Janice, I hope YOU yourself worked it out):

let x represent the weight in lbs of butter needed for recipe 1
let y ''                    ''                    ''                    '' recipe 2

x + y = 1

"One recipe takes 1/4 pound more than the other one"
so
x + (5/4)x = 1
(9/4)x = 1
x = 4/9   --> one recipe needs 4/9 lbs of butter

(4/9) + y = 1
y = 1 - (4/9)
y = 5/9     --> the other recipe needs 5/9 lbs of butter

im too tired right now to think about that other problem...

[xvimbi]

oh cmon janice, dont go on... blaming the puzzle.. haha"the bad workman blames his tools"
ok, Im gonna do the butter problem (and Janice, I hope YOU yourself worked it out):

let x represent the weight in lbs of butter needed for recipe 1
let y ''                    ''                    ''                    '' recipe 2

x + y = 1

"One recipe takes 1/4 pound more than the other one"
so
x + (5/4)x = 1
(9/4)x = 1
x = 4/9   --> one recipe needs 4/9 lbs of butter

(4/9) + y = 1
y = 1 - (4/9)
y = 5/9     --> the other recipe needs 5/9 lbs of butter

im too tired right now to think about that other problem...

Sorry, buddy:

one recipe needs 0.25 lbs more than the other =>
x+x+0.25=1
2x = 0.75
x = 0.375

recipe 1 needs 0.375 lbs
recipe 2 needs 0.625 lbs

[janice]

(sits back to watch Donjuan and Xvimbi duke it out!!)

[pianohopper]

DonJuan's mistake came in assuming that he could represent 1/4 more with (5/4)x. 

Use x as the variable for the recipe that uses less butter.  We know that x + 1/4 = y (the second recipe.)  Therefore, y cannot equal 5/4 x, because x would have to be 4/4, or 1 pound. 

-- so --

we must instead use substitution.  everywhere we see y, put in x + 1/4.  (or .25, as xvimbi said.) 

one recipe needs 0.25 lbs more than the other =>
x+x+0.25=1
2x = 0.75
x = 0.375

recipe 1 needs 0.375 lbs
recipe 2 needs 0.625 lbs

xvimbi is correct

[xvimbi]

(this one is significantly easier)
--My brother and I walk the same route to school every day.  My brother takes 40 minutes to get to school and I take 30 minutes.  Today, my brother left 5 minutes before I did. How long will it take me to catch up with him??

OK, so now this one:

The ratio between your speed and your brother's speed is 40/30 = 4/3. So, whatever takes your brother 4 minutes, takes you only 3 minutes. Therefore, it will take you 15 minutes for what your brother needs 20 minutes. That's the 5 minutes head start that your brother got. Thus, you'll catch him after 15 minutes.

I'll write up the analytical solution in a minute...

[xvimbi]

--My brother and I walk the same route to school every day.  My brother takes 40 minutes to get to school and I take 30 minutes.  Today, my brother left 5 minutes before I did. How long will it take me to catch up with him??

Analytical solution:

vb = brother's speed
vs = sister's speed
db = distance covered by brother
ds = distance covered by sister
tb = time used by brother
ts = time used by sister

db = ds = vb*tb = vs*ts
vb*(ts+5) = vs*ts
vb*ts + 5vb = vs*ts
5vb = vs*ts - vb*ts
5vb = ts(vs-vb)
ts = 5vb/(vs-vb)
1/ts = (vs-vb)/(5vb) = vs/(5vb) - 1/5
since (vs/vb) = 40/30 = 4/3
1/ts = 4/15 - 1/5 = 4/15 - 3/15 = 1/15
=> ts = 15

Voila!

[donjuan]

doh! i dont know why I even try...

  that's Canadian education for you!

[abell88]

doh! i dont know why I even try...

that's Canadian education for you!

What's that...the bad workman blames his education???

[donjuan]

What's that...the bad workman blames his education???

exactly 

in calculus, I kept asking questions and the teacher just kept on going "I'll have to get back to you on that" and she never did.

Before I knew it, the final was the next day

[thalbergmad]

MATHS QUESTION

What is the square root of 69??

[janice]

Ok guys, I will put you out of your misery!!  I'm sure that some will debate this, so I will just stay out of it and let you guys debate among yourselves!!  lol

Back to the dieter #1 and dieter #2 dilemma:

       d1 lost 1/8 of his weight, or 19 lbs. 
 
       We say 1/8 = 19/x where x=d1's original weight.
 
       So, you are correct when you solve:
 
       (Cross multiplying, then dividing:)  19 * 8 = 152  --> 152/1=152  --> x=152
 
       NOW...
 
       d2 weighs 2 lbs more than 152, or 154, after losing 1/6 of her original weight.              What was her original weight?
 
       Let x= d2's original weight
We know that her weight loss equals her original weight minus 154, or x-154=weight loss
and we know that she lost 1/6 of her original weight, or x/6, SO x/6 also = weight loss
 
       Now we have the equivalence:  x-154 = x/6  (weight loss equals weight loss)
(There are a number of ways you can go from here, but here's one...)
Subtract x from each side  -->  -154=x/6 - x
Since we know that the quantity x also equal x/1, we put x in the form of a fraction to facilitate subtract of fractions on the right side of the equation:
-154=((x/6)-(x-1))
In order to simplify the right side, we can subtract to find the difference x/6-x/1.  But first, of course, we must convet to like terms.  Using 6 as a common denominator, we rewrite the right side to ((x/6)-(6x/6)).
 
       We now have the equivalence of -154=((x/6)-(6x/6))  or  -154= (-5x/6)  (You have "x" sixths minus "6x" sixths = -5x sixths)
 
       Multiplying both side by 6 yields -924=(-5x)
       Dividing both sides by -5 yields x = 184.8 lbs
 
       You can check this by calculating as you did for d1.   1/6=x/154  -->  We think weight loss - 184.8-154 or 30.8lbs so 1/6=30.8/154 which is true.
 
 
 
 
 
 

[xvimbi]

Ok guys, I will put you out of your misery!!  I'm sure that some will debate this, so I will just stay out of it and let you guys debate among yourselves!!  lol

You have obviously not read any of our posts

[janice]

You have obviously not read any of our posts

Of course I have!!  And with great amusement!!

I just thought that the "proper" thing for me to do would be to post the answer (or should I say, "my" answer as opposed to "the" answer!!  Like I said, I could very well be wrong, and I will shut up and let you guys continue to debate among yourselves!  I posted it because it made many people think!!)

[donjuan]

Of course I have!!  And with great amusement!!

I just thought that the "proper" thing for me to do would be to post the answer (or should I say, "my" answer as opposed to "the" answer!!  Like I said, I could very well be wrong, and I will shut up and let you guys continue to debate among yourselves!  I posted it because it made many people think!!)

sorry to disappoint you, but the argument (if you really want to call it that) is long over.

If we were arguing, it was over how to comprehend your question..

[goansongo]

I agree with xvimbi on this one.  He was right from the start.  The last statement "We know #1 weighs 152 and dieter 2 weighs 154...but what did dieter 2 weigh before losing the weight???"  Should not be there because it messes up the problem.  It should say "#1 weights 152 BEFORE the diet (133lb AFTER the diet). "   That means...  #2 should weigh 162lb BEFORE the diet and 135lb AFTER the diet.  So #2 lost 27lb. 

Either Janice added in that last statement because she thought it was correct and consistent.  OR that last statement is added in because this is supposed to be a riddle with no answer.  It's just supposed to make you think about the different ways you can view this problem.