document.write( "Question 1142975: Isabel invested $8000. part in an account paying 6% interest and part in bonds paying 8%. If she has reversed the amounts invested, she would have received $100 less. How much did she invest in cash? \n" ); document.write( "

Algebra.Com's Answer #763707 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "Let x = invested at 6%.\r\n" );
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document.write( "Then the amount invested at 8% is  (8000 -x).\r\n" );
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document.write( "The total interest in this case is  0.06x + 0.08*(8000-x).\r\n" );
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document.write( "In the reversed case, the total interest is  0.08x + 0.06*(8000-x).\r\n" );
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document.write( "The difference is $100:\r\n" );
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document.write( "    0.06x + 0.08*(8000-x) = 0.08x + 0.06*(8000-x) + 100.\r\n" );
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document.write( "Simplify and solve for x:\r\n" );
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document.write( "    0.06x + 640 - 0.08x = 0.08x + 480 - 0.06x + 100\r\n" );
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document.write( "    640 - 0.02x = 0.02x + 580\r\n" );
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document.write( "    640 - 580 = 0.02x + 0.02x\r\n" );
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document.write( "    60        = 0.04x\r\n" );
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document.write( "     x        =  = 1500.\r\n" );
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document.write( "ANSWER.  $1500 invested at 6% and the rest 8000-1500 = 6500 dollars invested at 8%.\r\n" );
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document.write( "CHECK.  0.06*1500 + 0.08*6500 = 610 dollars.\r\n" );
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document.write( "        0.06*6500 + 0.08*1500 = 510 dollars.\r\n" );
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document.write( "        The difference is exactly $100  ---->   hence, the solution is correct !\r\n" );
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