SOLUTION: Silvia wants to mix 40% apple juice drink with pure apple juice to make 4L of a juice drink that is 90% apple juice. How much pure apple juice should she use? Express answer as a m

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Question 1127082: Silvia wants to mix 40% apple juice drink with pure apple juice to make 4L of a juice drink that is 90% apple juice. How much pure apple juice should she use? Express answer as a mixed number or fraction in simplest terms, if necessary.
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
Let x be the volume of the pure apple juice to be added, in liters.


Then the volume of the 40% juice to be mixed is (4-x) liters.


Your equation is


    0.4*(4-x) + x = 0.9*4


saying that the sum of amounts of the pure apple juice in both input ingredients is equal to that in resulting mix.


Simplify and solve the equation

    1.6 - 0.4x + x = 3.6

    0.6x = 3.6 - 1.6

    0.6x = 2

    x =  =  =  = .


Answer.   liters of the pure apple juice should be added.


Check.    = 0.9,  or 90% concentration.   ! Correct !

Solved.

-------------------

It is a standard and typical mixture problem.

For introductory lessons covering various types of mixture word problems see
    - Mixture problems
    - More Mixture problems
    - Solving typical word problems on mixtures for solutions
    - Typical word problems on mixtures from the archive
in this site.

You will find there ALL TYPICAL mixture problems with different methods of solutions,
explained at different levels of detalization,  from very detailed to very short.

Read them and become an expert in solution mixture word problems.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this textbook in the section "Word problems" under the topic "Mixture problems".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.


Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Here is a simple alternative to the standard algebraic method for solving mixture problems. If you understand how to use it, you will get to the answer much faster and with far less work.

Here is the whole solution process by this alternative method.

(1) 90% is 5/6 of the way from 40% to 100%. (Do some simple mental calculations: 90-40 = 50; 100-40 = 60; 50/60 = 5/6)

(2) Therefore, 5/6 of the mixture must be the higher percent juice.

(3) 5/6 of 4 liters is 20/6 = 10/3 liters.

ANSWER: 10/3 liters of pure apple juice
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