Question 1208723
<pre>
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?

 *[illustration ADC_1208723].

<font color = red><font size = 4><b><u>From the above TABLE:</font></font></b></u>
Start: Amount of acid: 800 mL ; amount of water: 200 mL ; Total in solution: 800 + 200 = 1,000 mL ; % acid: {{{matrix(1,7, 800/"1,000", "=", 4/5, "=", .8, or, "80%")}}} 
                                                                                                    % water: {{{matrix(1,7, 200/"1,000", "=", 1/5, "=", .2, or, "20%")}}}
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
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.
       Acid in solution: {{{matrix(1,5, 560/"1,000", "=", 56/100, "=", "56%")}}} ; Water in solution: {{{matrix(1,5, 440/"1,000", "=", 44/100, "=", "44%")}}}
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
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.
       Acid in solution: {{{matrix(1,3, 336/"1,000", "=", "33.6%")}}} ; Water in solution: {{{matrix(1,3, 664/"1,000", "=", "66.4%")}}}
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
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 = <font color = red><font size 
 = 4><b>697.6 mL</font></font></b>, is <font color = red><font size = 4><b>water</font></font></b>. 

       I hope you're able to follow this!

Sir Edwin,
Where @Ikleyn says the error is, is NOT where it is. I'll copy part of yours to show you the errors. 


<font color="red"><b>Ruth again thinks the solution is still too strong, so again she drains 100 mL from the beaker,</b></font>  

 liquid =  1000-100=900 mL
   acid =  (900)(0.336) = 302.4 mL <font color="blue"><b><==== The error is NOT HERE, as per @Ikleyn. This is FINE!</b></font>  

  water =  664-100=564 mL  <font color="blue"><b><==== The error is HERE. 100 mL was DRAINED, so 100 mL should NOT HAVE been
                                 subtracted from water. In fact, the REMAINING 900 mL, after 100 mL was drained
                                 includes 302.4 mL (33.6%) acid, and 597.6 (900 - 302.4) mL, or 66.4% water.</b></font> 
 % acid =  33.6% 
% water =  66.4% 

<font color="red"><b>and adds 100 mL of water.</b></font>  

 liquid =  900+100=1000 mL 
   acid =  302.4 mL
  water =  564+100=664 mL <font color="blue"><b><==== Instead of 564 mL HERE, the STARTING amount of water should be 597.6 mL; and,
                                with 100 mL ADDED, water becomes 597.6 + 100 = 697.6 mL!</b></font> 
 % acid =  302.4/1000 0.3024=30.24% 
% water =  664/1000 = 0.664 = 66.4% <font color="blue"><b><==== Instead of 664/1,000, this should be 697.6/1,000 = 69.76%, which makes
                                          FINAL acid and water percentages, 30.24 and 69.76, for a TOTAL of 100%.</b></font> 

<font color="red"><b>How many mL of water are now in the beaker?</b></font> 

664 mL   <-- ANSWER
697.6 mL <-- ANSWER <font color="blue"><b><==== Should be.</b></font> 

Edwin</pre>