Question 1184118
.
How much of​ a(n) 60% orange juice drink must be mixed with 9 gallons of a 40% orange juice drink 
to obtain a mixture that is 50% orange​ juice?
The amount of 60% orange juice drink is x gallons.
​(Type an integer or a​ decimal.)
Please help me find "x" thank you
~~~~~~~~~~~~~~~~~~


<pre>
If the amount of the 60% juice is x gallons, the the total volume of the final mixture is (x+9) gallons.


x gallons of the 60% juica contain  0.6x   gallons of the pure juice.

9 gallons of the 40% juica contain  0.4*9  gallons of the pure juice.


The final mixture should contain  0.5(x+9)  gallons of the pure juice.


Now you write equation


    0.6x + 0.4*9 = 0.5(x+9),


saying that the total of pure juice in ingredients is the same as it is in the final mixture.


    +--------------------------------------------------------------+
    |    As soon as you get this equation, the setup is complete,  |
    |            and now your task is to solve it.                 |
    +--------------------------------------------------------------+


From the equation


    0.6x - 0.5x = 0.5*9 - 0.4*9

        0.1x    =     0.9

           x    =     0.9/0.1 = 9.


<U>ANSWER</U>.  9 gallons of the 60% juice must be mixed.
</pre>

Solved.


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


It is a standard and typical mixture problem.


For introductory lessons covering various types of mixture word problems see

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Mixture-problems.lesson>Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/More-Mixture-problems.lesson>More Mixture problems</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-mixture-problems.lesson>Solving typical word problems on mixtures for solutions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/word/mixtures/Typical-word-problems-on-mixtures-from-the-archive.lesson>Typical word problems on mixtures from the archive</A>

in this site.


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


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


Also, &nbsp;you have this free of charge online textbook in ALGEBRA-I in this site

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-I - YOUR ONLINE TEXTBOOK</A>.


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



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.