SOLUTION: You have 6 liters of a pineapple juice blend that has 50% pure pineapple juice. How many liters of pure pineapple juice needs to be added to make a juice blend that is 75% pineapp

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Question 1169987: You have 6 liters of a pineapple juice blend that has 50% pure pineapple juice. How many
liters of pure pineapple juice needs to be added to make a juice blend that is 75% pineapple
juice?
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39621) About Me  (Show Source):
You can put this solution on YOUR website!
Using 1%2F2 for 50%, and 3%2F4 for 75%, and 1 for 100%,

If unknown v liters of pure juice to add,
%281%2F2%29%2A6%2B1%2Av=%283%2F4%29%28v%2B6%29
Solve for v.

highlight%28v=6%29

Answer by ikleyn(52817) About Me  (Show Source):
You can put this solution on YOUR website!
.
You have 6 liters of a pineapple juice blend that has 50% pure pineapple juice. How many
liters of pure pineapple juice needs to be added to make a juice blend that is 75% pineapple juice?
~~~~~~~~~~~~~~~~ 


The original blend contains 0.5*6 liters = 3 liters of the pure juice.


Let x be the volume of the pure juice you add to the original blend.


Then the final mixture contains (3+x) liters of the pure juise and has the total volume of (6+x) liters.


You want to have 75% concentration, which means

    %283%2Bx%29%2F%286%2Bx%29 = 0.75.


It is your basic (setup) equation to find x.  To solve it, multiply both sides by (6+x) and simplify

    3 + x = 0.75(6+x)

    3 + x = 4.5 + 0.75x

    x - 0.75x = 4.5 - 3

    0.25x     = 1.5

        x     = 1.5%2F0.25 = 6.


ANSWER.  6 liters of the pure juice to add.


CHECK.  %283%2B6%29%2F%286%2B6%29 = 9%2F12 = 3%2F4 = 0.75 = 75%.    ! Precisely correct !

Solved.