document.write( "Question 1136842: Alpha has £160 more than beta. After giving1/10 of his money to Beta, Alpha has three times as much money as Beta. How much money do they each have to start with? \n" ); document.write( "

Algebra.Com's Answer #754656 by ikleyn(52852) $\"\"$ $\"About$

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document.write( "a = b + 160                 (1)\r\n" );
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document.write( "a - 0.1a = 3*(b + 0.1a)     (2)\r\n" );
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document.write( "Equation (2) is equivalent to\r\n" );
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document.write( "0.9a = 3b + 0.3a      or\r\n" );
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document.write( "0.9a - 0.3a = 3b,\r\n" );
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document.write( "0.6a = 3b                   (3)\r\n" );
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document.write( "From eq(1), substitute a = b+160 into eq(3).\r\n" );
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document.write( "0.6*(b+160) = 3b\r\n" );
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document.write( "0.6*b + 0.6*160 = 3b\r\n" );
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document.write( "0.6*160 = 3b - 0.6b\r\n" );
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document.write( "96           = 2.4*b\r\n" );
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document.write( "b            =  = 40.\r\n" );
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document.write( "ANSWER.  Beta started with £40;  Alpha started with  £40 + £160 = £200.\r\n" );
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document.write( "CHECK.   200 - 20 = 180;  40 + 20 = 60.   180 is three times 60.   ! Correct !\r\n" );
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