Question 1209458
<pre>
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?

<font color="blue">Bob and John had some cards.</font> 

Bob has B cards. John has J cards

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

J-32 = B + 32

<font color="blue">If Bob gave John 163 cards then John would have 4 times as many cards as Bob.</font>

4(B-163) = J+163

<font color="blue">How many cards did Bob have?</font> 

{{{system(J-32=B+32, 4(B-163) = J+163)}}}

{{{system(J-B=64, 4B-652 = J+163)}}}

{{{system(J-B=64, -J+4B=652+163)}}}

{{{system(J-B=64, -J+4B=815)}}}

Adding the equations term by term,

{{{3B=879}}}

{{{B = 879/3 = 293}}}

<font size=6><b>So Bob had 293.    <--ANSWER</b></font>

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

{{{J-B=64}}}
{{{J-293=64}}}
{{{J=64+293}}}
{{{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</pre>