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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 $200$ mL from the beaker, adds $200$ mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains $200$ mL from the beaker, and adds $200$ mL of water. How many mL of water are now in the beaker?

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Answer :

sqdancefan

Answer:

  488 mL

Step-by-step explanation:

You want to know the number of mL of water in a beaker that begins with 800 mL of acid and 200 mL of water, after 200 mL of solution is replaced with water twice.

Dilution

Each step of the dilution process removes 20% of the beaker contents, keeping 80%, and replaces the removed amount with water. That is, the amount of water w' after the replacement is ...

  w' = 0.80×w +200 . . . . . . milliliters

We start with w0 = 200 mL of water in the beaker.

After the first dilution, the amount of water is ...

  w1 = 0.80×200 +200 = 360 . . . . . . mL

After the second dilution, the amount of water is ...

  w2 = 0.80×360 +200 = 488 . . . . . . mL

There are now 488 mL of water in the beaker.

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