SOLUTION: Hi sam had 2/3 of the amount of money bob had. David had twice as much money as sam. Sam spent half his money. If sam spent $48 less than david, both of them had the same amount o

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Question 1109667: Hi
sam had 2/3 of the amount of money bob had. David had twice as much money as sam. Sam spent half his money. If sam spent $48 less than david, both of them had the same amount of money left.
how much did sam spend.
how much did the 3 of them have at first.
Thanks
Found 3 solutions by ankor@dixie-net.com, TeachMath, greenestamps:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website!
sam had 2/3 of the amount of money bob had.
s = b
David had twice as much money as sam.
d = 2s
Sam spent half his money. If sam spent $48 less than david, both of them had the same amount of money left.
s = d - 48
s = 2(d-48)
replace d with 2s
s = 2(2s-48)
s = 4s - 96
96 = 4s - s
96 = 3s
s = 96/3
s = 32
how much did sam spend.
spent half so he spent 32/2 = $16
how much did the 3 of them have at first.
Sam:
s = $32,
then David
2(32) = $64
and Bob
b = 32
b = 32 *
b = $48

Answer by TeachMath(96)   (Show Source):
You can put this solution on YOUR website!

Correct answer: Original amount for Bob: $72
Original amount for Sam: $48
Original amount for David: $96

Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!

(1) At best, the problem is worded poorly. In my opinion it is worded incorrectly.

When it says "Sam spent $48 less than David", correct grammar implies that David spent something -- but the problem doesn't say anything about that.

A correct statement of the problem would have said something like "If Sam spent $48 less than David had,..."

(2) I would avoid fractions, to make the arithmetic easier. Where the first sentence says Sam had 2/3 of the amount that Bob had, I would start the problem with

let 2x = the amount Sam had
let 3x = the amount Bob had

Then since the problem says David had twice as much as Sam...

let 4x = the amount David had

Now, Sam spent half his money, which is x. The problem (worded correctly) says that is $48 less than what David had, so

Sam had 2x = $32
Bob had 3x = $48
David had 4x = $64

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(3) Another note for tutor teachmath.... I hope you are seeing these notes from me and will do something about changing the types of "answers" you give:

Giving correct answers without showing any work is of no use to the reader who asked the question.

Giving wrong answers without showing any work is worse....

If, in this case, you had an interpretation of the problem that leads to the answers you show, then showing the work you did to get your answer will be of use to the reader. Although I doubt it in this case, your interpretation might be the right one.