Question 1208723
<pre>
First, I'll copy and paste your problem here so I can delete those "$" dollar
marks around every number.  They confuse me. We didn't do that where I came
from. <font face="wingdings">J</font>


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?

I'll keep track of the liquid, acid, water, % acid, and % water, because in
other problems like this you might be asked different amounts and percentages.
 
<font color="red"><b>Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water.</b></font> 

 liquid = 800+200 = 1000 mL
   acid = 800 mL
  water = 200 mL
 % acid = 800/1000 = 0.8 = 80%
% water = 200/1000 = 0.2 = 20% 

<font color="red"><b>She thinks the solution is a little strong, so she drains 300 mL from the beaker,</b></font>  

 liquid =  1000-300 = 700 mL
   acid =  (0.8)(700) = 560 mL
  water =  (0.2)(700) = 140 mL
 % acid =   80%
% water =   20% 

<font color="red"><b>adds 300 mL of water, and stirs the solution.</b></font>  

 liquid =  700+300 = 1000 mL
   acid =  560 mL
  water =  140+300 = 440 mL
 % acid =  560/1000 = 0.56 = 56%
% water =  440/1000 = 0.44 = 44% 

<font color="red"><b>Ruth thinks the solution is still too strong, so again she drains 400 mL from the beaker,</b></font>  

 liquid =  1000-400 = 600 mL
   acid =  (600)(0.56) = 336 mL
  water =  (600)(0.44) = 264 mL
 % acid =  56%
% water =  44% 

<font color="red"><b>and adds 400 mL of water.</b></font>  

 liquid =  600+400=1000 mL
   acid =  336 mL
  water =  264+400=664 mL
 % acid =  336/1000=33.6% 
% water =  664/1000=66.4% 


<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
  water =  664-100=564 mL
 % 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
 % acid =  302.4/1000 0.3024=30.24% 
% water =  664/1000 = 0.664 = 66.4% 

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

664 mL   <-- ANSWER

Edwin</pre>