SOLUTION: A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 85% pure antifreeze

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Question 1144712: A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 85% pure antifreeze. The company wants to obtain 170 gallons of a mixture that contains 15% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?

Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
v gallons of the prem. 85%
170-v gallons of just water

85v%2B0%28170-v%29=15%2A170

85v=15%2A170

highlight%28v=30%29---------gallons of the 85%, premium antifreeze.
highlight%28140%29 gallons water.

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the volume of the premium 85% antifreeze (in gallons) and

let y be the volume of water.


        x + y  = 170       gallons     (1)   (total volume equation)

    0.85x      = 0.15*170   gallons    (2)   (pure antifreeze volume equation)


From equation (2),  x = %280.15%2A170%29%2F0.85 = 30.


Then from (1),  y = 170-30 = 140 gallons.


ANSWER.  140 gallons of water.


The same solution can be presented in wording form.

Since they simply DILUTE the existing mixture, the content of the pure antifreeze remains the same: it is  170%2A0.15 = 25.5 gallons.


Hence, the 85% premium antifreeze should have the volume of  25.5%2F0.85 = 30 gallons to be 85% mixture.


The complement to 170 gallons, i.e.  170 - 30 = 140 gallons, is the water volume, which should be added.

You get the same answer.