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Algebra Level 5

My father had to wash some nappies in a strong bleach solution and wanted to rinse them out so that they contained as small a concentration of bleach as possible. He can wring the nappies out so there is just half a litre of liquid left. He wrings the nappies out after washing them in the bleach, adds 12 litres of water, mixes thoroughly, wrings them out again, adds a further 8 litres of water, and mixes thoroughly, reducing the concentration of bleach to 1 k \dfrac {1}{k} of its original. Find k k .


The answer is 425.

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Sharky Kesa by Sharky Kesa , 19, United Kingdom

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1 solution

.5 liter remains after wringing out. Add 12 makes total 12.5 liters. So consentrarion is .5/12,5=1/25. But after wringing only .5 liter of this concentration remains. That is in .5 remaining, only .5/25 of liquid is present. That is 1/50 of liquid in total of 8.5. So the concentration is (1/50)/8.5=1/425. k=425.

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concentration of bleach in the solution is like x:y -> x/(x+y) amt of bleach and y/(x+y) amt of water in .5 litr of such solution there is x/(2 (x+y) amt of bleach adding 12 lits water it becomes: x/2 : y/2 +12 -> x/ (x+y+6) amt of bleach.. in half of it, there is: x/ (2 (x+y+6) ) amt of bleach. and rest is water... =(y+6)/2 (x+y+6) adding 8 ltr of water the water becomes => 8 + { y+6 /2 (x+y+6)} = (16x +16y +84+y+6)/ 2 (x+y+6) = (16x+17y +90 )/ 2 (x+y+6)

total amount of liquid : {x/ 2 (x+y+6) } + {16x +17y +90/ 2 (x+y+6)} = 17x +17y +90/ 2*(x+y+6)

thus bleach concentration, in comparison to original, becomes: [ { x/ 17x + 17y + 90} / x/ (x+y) ] = 1/k x+y / {17(x+y)+90} = 1/k now what was y in relation to x or in absolute amount, will tell the actual result.

where am i wrong?? please enlighten me.

Ananya Aaniya - 5 years, 10 months ago

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I think your x/(2(x+y)) is not correct. First .5 liter is not the mix but bleach itself. You may see my solution. You are welcome back if you did not follow any of the steps or with other difficulty..

Niranjan Khanderia - 5 years, 10 months ago

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