<PRE><B>Question 205842</B>
A has $x and B has $y. If A gives B $3, B will have 2 times as much as A. If B gives A $6, A will have $4 more than B.
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First, we look at:
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&gt;&gt;...A has $x and B has $y. If A gives B $3,...&lt;&lt;
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...then, A will have $(x-3), and B will have $(y+3)...
&lt;/pre&gt;&lt;/font&gt;&lt;/b&gt;
&gt;&gt;...B will have 2 times as much as A...&lt;&lt; 
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...so $(y+3) will be 2 times $(x-3), or

             (y+3) = 2(x-3)
&lt;/pre&gt;&lt;/font&gt;&lt;/b&gt;
&gt;&gt;...A has $x and B has $y... If B gives A $6,...&lt;&lt;
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...then, B will have $(y-6), and A will have $(x+6)...
&lt;/pre&gt;&lt;/font&gt;&lt;/b&gt;
&gt;&gt;... A will have $4 more than B...&lt;&lt; 
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...so $(x+6) will be $(y-6)+4, or

             (x+6) = (y-6)+4

So we have this system of equations:

{{{system((y+3)=2(x-3),(x+6)=(y-6)+4)}}}

Simplifying:

{{{system(y+3=2x-6,x+6=y-6+4)}}}

{{{system(y=2x-9,x+6=y-2)}}}

{{{system(y=2x-9,x=y-8)}}}

Solve by substitution and get

{{{x=17}}}, {{{y=25}}}

So A has $17 and B has $25.

Checking:
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&gt;&gt;...If A gives B $3,...&lt;&lt; 
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then A will have $14, and B will have $28.
&lt;/pre&gt;&lt;/font&gt;&lt;/b&gt;
&gt;&gt;...B will have 2 times as much as A...&lt;&lt;
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And yes, indeed, $28 will be 2 times $14.
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&gt;&gt;...If B gives A $6,...&lt;&lt;
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then B will have $19, and A will have $23
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&gt;&gt;...A will have $4 more than B...&lt;&lt;
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And, yes indeed, $23 is $4 more than $19.

Edwin&lt;/pre&gt;


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