Question 1169987
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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?
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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

    {{{(3+x)/(6+x)}}} = 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     = {{{1.5/0.25}}} = 6.


<U>ANSWER</U>.  6 liters of the pure juice to add.


<U>CHECK</U>.  {{{(3+6)/(6+6)}}} = {{{9/12}}} = {{{3/4}}} = 0.75 = 75%.    ! Precisely correct !
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Solved.