Question 1209458
<pre>
<font color="green">Bob and John had some cards.</font> 

Bob has B cards. John has J cards

<font color="green">When John gave Bob 32 cards then they would have an equal amount of cards.</font>

J-32 = B + 32

<font color="green">If Bob gave John 161 cards then John would have 4 times as many cards as Bob.</font>

4(B-161) = J+161

<font color="green">How many cards did Bob have.</font> 

{{{system(J-32=B+32, 4(B-161) = J+161)}}}

{{{system(J-B=64, 4B-644 = J+161)}}}

{{{system(J-B=64, -J+4B=644+161)}}}

{{{system(J-B=64, -J+4B=805)}}}

Adding the equations term by term,

{{{3B=869}}}

{{{B = 869/3 = 289&2/3}}}

That's what I got, also.

{{{J-869/3=64}}}
{{{J=64+869/3}}}
{{{J=192/3+869/3}}}
{{{J=761/3=253&2/3}}}

Maybe they cut some cards up.

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

<font color="green">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?</font>

Let's do it that way:
After John gave Bob 32 cards, they had N cards each.
<font color-"green>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.</font>

{{{4(N-161)=N+161}}}

{{{4N-644=N+161}}}

{{{3N=805}}}

{{{N=805/3=268&1/3}}}

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

So in the beginning, John had {{{268&1/3+32=300&1/3}}} and
Bob had {{{268&1/3-32=236&1/3}}}

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</pre>