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# help stuck

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Help I'm really stuck here

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 150 mL from the beaker, adds 150 mL of water, and stirs the solution. Ruth thinks the solution is still too strong, so again she drains 150 mL from the beaker, and adds 150 mL of water. How many mL of water are now in the beaker?

Aug 25, 2023

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She starts with 1000ml of solution

Initially   the   ratio of  water to  acid  is    200 : 800   =   1 : 4

When she pours off 150 ml  of solution the first time she now has   850 ml of solution

The ml of  water now  =  1 /( 1 + 4) *(850)  =  1/5 * 750 =  170ml

And the ml of acid =  850 - 170  = 680 ml

Note that the ratio of water to  acid is still 170 : 680 =  1 : 4

When she adds 150  ml of water the first time she now  has 1000ml again

But now she has 170 + 150 =  320 ml of water  (the acid  amt hasn't changed)

The new ratio of water to  acid is 320 : 680  =  8 : 17

The second time she  pours off 150ml  the ratio of water to  acid has not changed

She now has 850 ml of solution

The ml of  water is now  8 / ( 8 + 17) * 850  = 272

The ml of acid is 850 - 272  =  578 ml

Finally ....adding back  150 ml of water  gives us 1000 ml again

She now has  272 + 150 =  422 ml of  water

And she still has 578 ml of acid

So  she ends up with 422 ml of water  and  578 ml of acid

The final ratio of water to acid is   422 : 578  =  211 : 289   Aug 25, 2023