One canned juice drink is 30% orange juice; another is 5% orange juice. how many liters of each should be mixed together in order to get 25L that is 6% orange juice?

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tjbrewer | Elementary School Teacher | (Level 2) Associate Educator

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To get the appopriate concentration we use x to stand for parts of the 30% concentration and y to stand for parts of the 5% concentration, and we get the following equation `.06=(.3x+.05y)/(x+y)` And we want 25 L so we want `x+y=25` L.  We plug that value into our equation and we get `.06=(.3x+.05y)/25` we express .06 in fraction form and cross multiply `6/100=(.3x+.05y)/25 --->150=30x+5y` we solve this equation for y to get `y=-6x+30` then we take the other equation `x+y=25` and we solve it for y to get `y=-x+25` we plug this into the other equation and we get `-x+25=-6x+30` we solve for x and we find `x=1` We insert that back into x+y=25, and we find y =24. 

You need 1 Liter of the 30% juice and 24 Liters of the 5% juice to get 25 liters of 6% juice.