document.write( "Question 1208723: Ruth has a beaker containing a solution of $800$ mL of acid and $200$ mL of water. She thinks the solution is a little strong, so she drains $300$ mL from the beaker, adds $300$ mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains $400$ mL from the beaker, and adds $400$ mL of water. Ruth again thinks the solution is still too strong, so again she drains $100$ mL from the beaker, and adds $100$ mL of water. How many mL of water are now in the beaker? \n" ); document.write( "

Algebra.Com's Answer #847332 by MathTherapy(10552) $\"\"$ $\"About$

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document.write( "Ruth has a beaker containing a solution of $800$ mL of acid and $200$ mL of water.  She thinks the solution is a little strong, so she drains $300$ mL from the beaker, adds $300$ mL of water, and stirs the solution.  Ruth thinks the solution is still too strong, so again she drains $400$ mL from the beaker, and adds $400$ mL of water.  Ruth again thinks the solution is still too strong, so again she drains $100$ mL from the beaker, and adds $100$ mL of water.  How many mL of water are now in the beaker?\r\n" );
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document.write( "From the above TABLE:\r\n" );
document.write( "Start: Amount of acid: 800 mL ; amount of water: 200 mL ; Total in solution: 800 + 200 = 1,000 mL ; % acid:  \r\n" );
document.write( "                                                                                                    % water: \r\n" );
document.write( "1.     DRAINING 300 mL of solution: 1,000 - 300 = 700 mL of solution left, of which 560 mL is acid and 140 mL is water\r\n" );
document.write( "2.     ADDING 300 mL of water: Solution = 700 + 300 = 1,000 mL, of which 560 mL is STILL acid and 140 + 300 = 440 mL, is water.\r\n" );
document.write( "       Acid in solution:  ; Water in solution: \r\n" );
document.write( "3.     DRAINING 400 mL of solution: 1,000 - 400 = 600 mL of solution left, of which 56%, or 336 mL is acid and 264 mL is water\r\n" );
document.write( "4.     ADDING 400 mL of water: Solution = 600 + 400 = 1,000 mL, of which 336 mL is STILL acid and 264 + 400 = 664 mL, is water.\r\n" );
document.write( "       Acid in solution:  ; Water in solution: \r\n" );
document.write( "5.     DRAINING 100 mL of solution: 1,000 - 100 = 900 mL of solution left, of which 33.6%, or 302.4 mL is acid, and 900 - 302.4, or 597.6 mL is water\r\n" );
document.write( "6.     Finally, ADDING 100 mL of water: Solution = 900 + 100 = 1,000 mL, of which 302.4 mL is STILL acid and 1,000 - 302.4 = 697.6 mL, is water. \r\n" );
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document.write( "       I hope you're able to follow this!\r\n" );
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document.write( "Sir Edwin,\r\n" );
document.write( "Where @Ikleyn says the error is, is NOT where it is. I'll copy part of yours to show you the errors. \r\n" );
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document.write( "Ruth again thinks the solution is still too strong, so again she drains 100 mL from the beaker,  \r\n" );
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document.write( " liquid =  1000-100=900 mL\r\n" );
document.write( "   acid =  (900)(0.336) = 302.4 mL <==== The error is NOT HERE, as per @Ikleyn. This is FINE!  \r\n" );
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document.write( "  water =  664-100=564 mL  <==== The error is HERE. 100 mL was DRAINED, so 100 mL should NOT HAVE been\r\n" );
document.write( "                                 subtracted from water. In fact, the REMAINING 900 mL, after 100 mL was drained\r\n" );
document.write( "                                 includes 302.4 mL (33.6%) acid, and 597.6 (900 - 302.4) mL, or 66.4% water. \r\n" );
document.write( " % acid =  33.6% \r\n" );
document.write( "% water =  66.4% \r\n" );
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document.write( "and adds 100 mL of water.  \r\n" );
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document.write( " liquid =  900+100=1000 mL \r\n" );
document.write( "   acid =  302.4 mL\r\n" );
document.write( "  water =  564+100=664 mL <==== Instead of 564 mL HERE, the STARTING amount of water should be 597.6 mL; and,\r\n" );
document.write( "                                with 100 mL ADDED, water becomes 597.6 + 100 = 697.6 mL! \r\n" );
document.write( " % acid =  302.4/1000 0.3024=30.24% \r\n" );
document.write( "% water =  664/1000 = 0.664 = 66.4% <==== Instead of 664/1,000, this should be 697.6/1,000 = 69.76%, which makes\r\n" );
document.write( "                                          FINAL acid and water percentages, 30.24 and 69.76, for a TOTAL of 100%. \r\n" );
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document.write( "How many mL of water are now in the beaker? \r\n" );
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document.write( "664 mL   <-- ANSWER\r\n" );
document.write( "697.6 mL <-- ANSWER <==== Should be. \r\n" );
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document.write( "Edwin

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