SOLUTION: Hi Bob and John had some cards. When John gave Bob 32 cards then they would have an equal amount of cards. If Bob gave John 161 cards then John would have 4 times as many cards

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Question 1209458: Hi
Bob and John had some cards. When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 161 cards then John would have 4 times as many cards as Bob.
How many cards did Bob have.
My son found that Bob had 289 and two thirds cards.Can someone check this please.

Found 4 solutions by Edwin McCravy, ikleyn, timofer, mccravyedwin:
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
Bob and John had some cards. 

Bob has B cards. John has J cards

When John gave Bob 32 cards then they would have an equal amount of cards.

J-32 = B + 32

If Bob gave John 161 cards then John would have 4 times as many cards as Bob.

4(B-161) = J+161

How many cards did Bob have. 

system%28J-32=B%2B32%2C+4%28B-161%29+=+J%2B161%29

system%28J-B=64%2C+4B-644+=+J%2B161%29

system%28J-B=64%2C+-J%2B4B=644%2B161%29

system%28J-B=64%2C+-J%2B4B=805%29

Adding the equations term by term,

3B=869

B+=+869%2F3+=+289%262%2F3

That's what I got, also.

J-869%2F3=64
J=64%2B869%2F3
J=192%2F3%2B869%2F3
J=761%2F3=253%262%2F3

Maybe they cut some cards up.

-----------------

Or maybe there was another way to interpret this. Let's reword it this way:

Bob and John had some cards. 
John gave Bob 32 cards and then they had an equal amount of cards. 
Beginning with an equal number of cards, Bob gave John 161 cards. 
Then John had 4 times as many cards as Bob. 
How many cards did Bob have?

Let's do it that way:
After John gave Bob 32 cards, they had N cards each.
Bob gave John 161 cards. Then Bob had N-161 cards and John had N+161 cards.
Then John had 4 times as many cards as Bob.

4%28N-161%29=N%2B161

4N-644=N%2B161

3N=805

N=805%2F3=268%261%2F3

So originally John had 32 cards more and Bob had 32 cards less.

So in the beginning, John had 268%261%2F3%2B32=300%261%2F3 and
Bob had 268%261%2F3-32=236%261%2F3

That also requires cutting cards in thirds. 

I dunno.  Obviously, your son's teacher was not savvy as to how to 
make up word problems.

Edwin

Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
Bob and John had some cards.
When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 161 cards then John would have 4 times as many cards as Bob. How many cards did Bob have.
My son found that Bob had 289 and two thirds cards. Can someone check this please.
~~~~~~~~~~~~~~~~~~~~~~~ 

x = the number of cards Bob had initially.

Then the number of cards John had initially is (x+2*32) = (x+64).


"If Bob gave John 161 cards then John would have 4 times as many cards as Bob. "


In Math form, it means

       Bob had      John had
        after         after
        giving       getting

   4 * (x - 161)  = (x+64)+161.


Simplify and find x

    4x - 644 = x + 225,

    4x - x = 225 + 644,

       3x  =   869

        x  =   869/3 = 2892%2F3.

The answer that your son got is correct, but makes no sense,
since the number of cards must be a non-negative integer number.

It means that the problem, as posted, printed and presented, is HEAVILY DEFECTIVE.


/\/\/\/\/\/\/\/\/\/\/\


Comment from student : Hi ikleyn Thank you for confirming the absurd answer. This is straight from the textbook.


My response : Report to the Publishing company or/and to the author, referring to
the precise textbook name, edition, year of edition, ISBN number,
then the section name, page number and the number of the problem.



Answer by timofer(105) About Me  (Show Source):
You can put this solution on YOUR website!
"When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 161 cards then John would have 4 times as many cards as Bob.
How many cards did Bob have."

system%28j-32=b%2B32%2C4%28b-161%29=j%2B161%29

system%28j=b%2B64%2C4%28b-161%29=j%2B161%29

4%28b-161%29=b%2B64%2B161

4%28b-161%29=b%2B225

4b-4%2A161=b%2B225

4b=b%2B225%2B4%2A161

3b=225%2B4%2A161

b=289%262%2F3

The description or the question is wrong.

Answer by mccravyedwin(408) About Me  (Show Source):
You can put this solution on YOUR website!
I think the error was that 161 should have been 163.  The answer
comes out a whole number when you change 161 to 163.

So I think the problem should have been:

Bob and John had some cards. When John gave Bob 32 cards then they would have an equal amount of cards.
If Bob gave John 163 cards then John would have 4 times as many cards as Bob.
How many cards did Bob have?

Bob and John had some cards. 

Bob has B cards. John has J cards

When John gave Bob 32 cards then they would have an equal amount of cards.

J-32 = B + 32

If Bob gave John 163 cards then John would have 4 times as many cards as Bob.

4(B-163) = J+163

How many cards did Bob have? 

system%28J-32=B%2B32%2C+4%28B-163%29+=+J%2B163%29

system%28J-B=64%2C+4B-652+=+J%2B163%29

system%28J-B=64%2C+-J%2B4B=652%2B163%29

system%28J-B=64%2C+-J%2B4B=815%29

Adding the equations term by term,

3B=879

B+=+879%2F3+=+293

So Bob had 293.    <--ANSWER

Let's find out how many cards John had so we can check.

J-B=64
J-293=64
J=64%2B293
J=357

Bob had 293 and John had 357. 

When John gave Bob 32 cards they an equal amount of cards.

John then had 357-32=325
Bob then had 293+32=325

Bob gave John 163 cards 

John then had 357+163=520
Bob then had 293-163=130

Checking (130)(4) = 520 

That shows John then had 4 times as many cards as Bob.

Edwin