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November 3rd, 2009, 10:48 AM   #1
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Carrot juice

Eric, a health enthusiast, enjoys mixing his own beverages. His current favorite is a carrot drink that contains 40% pure carrot juice. He has been to the store and has found some concentrated juice that is 60% pure carrot juice. His wife, Alicia, found some carrot juice on sale at a different health-food store, and she brought home 80 quarts. It contains 12% pure carrot juice. How many gallons of the concentrated 60% carrot juice does Eric need to add to the 80 quarts that Alicia brought home to produce his perfect drink containing 40% carrot juice?
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November 3rd, 2009, 11:58 AM   #2
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Re: Carrot juice

I am not familiar with gallons, I assume 1 gallon=4 quarts. If not - please change calculation properly.

we have 80 q of 12% juice, uknown amount of 60% to add to get 40% juice.

What we need is 40%=0,4 juice, so it mean 'pure juice'/volume=0,4
pure juice means how many 100% juice is in volume, for example in 12% 'juice per gallon)

So, we need 0,4 juice and volume would be 20g + V(where V=Volumen of 60% juice). Amount of juice would be 0,12x20g+0,6xV.
Do you follow?

So 0,4 = (0,12x20g+0,6*V)/(80+V)
calculate
0,4x20g+0,4V=2,4g+0,6V
8g-2,4g=0,2V
5,6g=0,2V
V=28g

Check


20g x 0,12 + 28 g x 0,6=2,4+16,6=19,2 juice/g (of 'pure' juice)
volume= 20g+28g=48g

concetration of mixed juice 19,2/48=0,4 = 40%
Get healthy
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November 3rd, 2009, 10:23 PM   #3
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Re: Carrot juice

Sorry! of course it should be So 0,4 = (0,12x20g+0,6*V)/(20+V)
(I put in quarts, not in gallons).
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