SOLUTION: a truck radiator holds 36L of fluid. How much pure antifreeze must be added to a mixture that is 4% antifreeze to fill the radiator with a mixture that is 20% antifreeze?

Question 163719: a truck radiator holds 36L of fluid. How much pure antifreeze must be added to a mixture that is 4% antifreeze to fill the radiator with a mixture that is 20% antifreeze?
Found 2 solutions by checkley77, gonzo:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
.04x+(36-x)=.2*36
.04x+36-x=7.2
-.96x=7.2-36
-.96x=-28.8
x=-28.8/-.96
x=30 L of 4% antifreeze is used.
36-30=6 L of pure antifreeze is used.
Proof:
.04*30+(36-30)=.2*36
1.2+6=7.2
7.2=7.2

Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
R = radiator = 36 Liters of mixture.
A = Antifreeze = .04 * 36 = 1.44 Liters of antifreeze
W = Water = .96 * 36 = 34.56 Liters of Water.
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a mixture of .20 Antifreeze would take 7.2 Liters of Antifreeze (.2*36).
this mixture would have 28.8 Liters of Water (.8*36).
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you need to add (7.2 - 1.44) Liters of Antifreeze which equals 5.76 Liters of Antifreeze.
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you also need to remove (34.56 - 28.8) Liters of Water which equals 5.76 Liters of Water.
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In order to remove 5.76 Liters of Water, you have to remove 5.76/.96 Liters of the original mixture. This equals 6 Liters of the original mixture.
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Removing 6 Liters of the original mixture also removes .04*6 Liters of Antifreeze. This equals .24 Liters of Antifreeze.
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Now you have to add 5.76 Liters of Antifreeze plus .24 Liters of Antifreeze that you removed. This equals 6 Liters of Antifreeze which just happens to be the amount of mixture that you removed.
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Your new mixture contains the following:
6 Liters of Antifreeze you added.
30 Liters of the original mixture.
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30 Liters of the original mixture contains .04 * 30 Liters of Antifreeze which equals 1.2 Liters of Antifreeze.
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6 Liters of Antifreeze you added plus 1.2 Liters of Antifreeze still in there makes 7.2 Liters of Antifreeze.
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You now have .2 * 36 Liters of Antifreeze = 7.2 Liters.
The rest is water which is .8 * 36 Liters of Water = 28.8 Liters.
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if there's an easier way to do this i haven't figured it out yet.
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Answer is you have to remove 6 Liters of the original mixture and you have to add 6 Liters of pure Antifreeze.
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