document.write( "Question 205842: 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. How much does A have? \n" ); document.write( "

Algebra.Com's Answer #155498 by Edwin McCravy(20065) $\"\"$ $\"About$

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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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document.write( "First, we look at:\r\n" );
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\n" ); document.write( ">>...A has $x and B has $y. If A gives B $3,...<<
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document.write( "...then, A will have $(x-3), and B will have $(y+3)...\r\n" );
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\n" ); document.write( ">>...B will have 2 times as much as A...<<
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document.write( "...so $(y+3) will be 2 times $(x-3), or\r\n" );
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document.write( "             (y+3) = 2(x-3)\r\n" );
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\n" ); document.write( ">>...A has $x and B has $y... If B gives A $6,...<<
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document.write( "...then, B will have $(y-6), and A will have $(x+6)...\r\n" );
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\n" ); document.write( ">>... A will have $4 more than B...<<
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document.write( "...so $(x+6) will be $(y-6)+4, or\r\n" );
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document.write( "             (x+6) = (y-6)+4\r\n" );
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document.write( "So we have this system of equations:\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "Solve by substitution and get\r\n" );
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document.write( "So A has $17 and B has $25.\r\n" );
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document.write( "Checking:\r\n" );
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\n" ); document.write( ">>...If A gives B $3,...<<
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document.write( "then A will have $14, and B will have $28.\r\n" );
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\n" ); document.write( ">>...B will have 2 times as much as A...<<
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document.write( "And yes, indeed, $28 will be 2 times $14.\r\n" );
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\n" ); document.write( ">>...If B gives A $6,...<<
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document.write( "then B will have $19, and A will have $23\r\n" );
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\n" ); document.write( ">>...A will have $4 more than B...<<
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document.write( "And, yes indeed, $23 is $4 more than $19.\r\n" );
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document.write( "Edwin

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