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Homework Help: Word Problem Question

  1. Oct 11, 2006 #1
    Ive got an assignment of word problems and cant seem to figure this one out:

    A 6 Litre car radiator is 2 thirds full of water. How much of a 90% antifreeze solution (90% is alcohol by volume) must be added to it to make a 10% antifreeze solution in the radiator?

    I came up with the equation: 0.9x=(0.1)(6)

    but that didnt work so any help about what the way to set up the problem would be great.
     
  2. jcsd
  3. Oct 11, 2006 #2

    Office_Shredder

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    How much water is in the radiator?
     
  4. Oct 11, 2006 #3
    4L of water
     
  5. Oct 11, 2006 #4
    i tried to do it a new way which was :

    4+0.9x=(0.1)(6)

    but i got a negative number from that attempt so that cant be the answer
     
  6. Oct 11, 2006 #5

    HallsofIvy

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    You are assuming that the total liquid volume in the radiator is 6 litres. If that were the case, that would mean that you were adding 2 litres of antifreeze solution. But then you would be adding .9(2)= 1.8 litres of pure antifreeze which would give a concentration of 1.8/6.0= 0.3 or 30%. That's too high so you must not be filling the radiator.

    Let x be the number of litres of 90% solution you are adding. Then the total liquid volume in the radiator is 4+ x litres. The amount of pure anti-freeze you are adding is (as you say) .9x. The concentration of pure anti-freeze in the radiator is [itex]\frac{.9x}{4+ x}= .1[/itex]. Solve that for x.
     
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