SOLUTION: You have a jug of 40% antifreeze solution in your garage, and you just bought a new container of 100% antifreeze from the auto parts store. You need to mix up 1 gallon of 50% anti

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Question 321890: You have a jug of 40% antifreeze solution in your garage, and you just bought a new container of 100% antifreeze from the auto parts store. You need to mix up 1 gallon of 50% antifreeze for your car's radiator. How much of each of the two solutions do you need to use?
Answer by Fombitz(32388) About Me  (Show Source):
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You have a jug of 40% antifreeze solution in your garage, and you just bought a new container of 100% antifreeze from the auto parts store. You need to mix up 1 gallon of 50% antifreeze for your car's radiator. How much of each of the two solutions do you need to use?
Let A be the amount of 40% solution, B the amount of 100% solution.
Volume equation:
1.A%2BB=1
Concentration equation:
40A%2B100B=50%281%29
2.4A%2B10B=5
Multiply eq. 1 by (-4) and add to eq. 2,
-4A-4B%2B4A%2B10B=-1%2B5
6B=4
B=4%2F6
highlight%28B=2%2F3%29
Then from eq. 1,
A%2B2%2F3=1
highlight%28A=1%2F3%29
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Use 1/3 gallon of 40% solution and 2/3 gallon of 100% solution.