document.write( "Question 1101871: Keith and Shawn each have some money. If Keith spends $38, the ratio of the amount of money Keith has to the amount of money Shawn has will become 2:5. If Shawn spends $38, the ratio will become 8:13. How much does each boy have? \n" ); document.write( "

Algebra.Com's Answer #716500 by ikleyn(52787) $\"\"$ $\"About$

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document.write( " = ,           (1)\r\n" );
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document.write( " = .          (2)\r\n" );
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document.write( "5*(K-38) = 2S,        (3)\r\n" );
document.write( "13K = 8*(S-38).       (4)\r\n" );
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document.write( " 5K - 2S =  5*38,     (5)\r\n" );
document.write( "13K - 8S = -8*38.     (6)\r\n" );
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document.write( "Multiply eq(5) by 4 (both sides). The modified system is\r\n" );
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document.write( "20K - 8S = 20*38,     (7)\r\n" );
document.write( "13K - 8S = -8*38.     (8)\r\n" );
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document.write( "Now subtract eq(7) from eq(8) (both sides). You will get\r\n" );
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document.write( "20K - 13K = 20*38 - (-8)*38,   or\r\n" );
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document.write( "7K = 20*38 + 8*38 = 28*38  ====>  K =  = 4*38 = 152.\r\n" );
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document.write( "Then from (5),  2S = 5K - 2*38 = 5*152 - 2*38 = 684  ====>  S =  = 342.\r\n" );
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document.write( "Answer.  K = 152,  S = 342.\r\n" );
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