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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 $300$ mL from the beaker, and adds $300$ mL of water.  How many mL of water are now in the beaker?

 Dec 16, 2023
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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 $300$ mL from the beaker, and adds $300$ mL of water.  How many mL of water are now in the beaker?

 

 

The  mixture originally  is  80% acid and 20% water

When she drains 300 ml  there are 700 ml  composed of (.80)(700) = 560ml of acid and (.20)(700) = 140ml of water

Adding 300 ml of water to this gives a solution composed of 560/1000 = 56% acid and (140 + 300) /1000 =

44% water ......so 560 ml are acid and 440ml are water

 

Draining 300 ml  of this  solution  gives us ( .56)(700) = 392ml of acid and (.44)(700) = 308ml of water

 

Adding back  300ml  of water gives us  308 + 300 =   608ml of water

 

cool cool cool

 Dec 16, 2023

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