Question 1045977
.
How many liters of an antifreeze that is 18% alcohol must be mixed with an antifreeze that is 10% alcohol to produce an antifreeze that is 15% alcohol
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<pre>
Let "x" be a volume of the 18% antifreeze and "y" be a volume of the 18% antifreeze to mix.

Then the total volume is x+y;

The volume of the pure antifreeze in x liters of the 18% antifreeze is 0.18*x;

The volume of the pure antifreeze in y liters of the 10% antifreeze is 0.10*y;

The volume of the pure antifreeze in the mixture is 0.18x + 0.10y.

The condition on the concentration of the mixture says and requires 

{{{(0.18x + 0.10y)/(x+y)}}} = 0.15,   or

0.18x + 0.1y = 0.15*(x+y),  or

0.18x - 0.15x = 0.15y - 0.1y,   or

0.3x = 0.5y,

Then y = {{{(0.3/0.5)*x}}} = {{{(3/5)*x}}},  or  {{{y/x}}} = {{{3/5}}}.


In other words, the ratio of the volume of the 10% antifreeze to the volume of the 18% antifreeze must be {{{3/5}}},  or  0.6.


For example, you can take 3 liters of the 10% antifreeze and 5 liters of the  18% antifreeze.

Let's check it:  {{{(0.1*3 + 0.18*5)/(3 + 5)}}} = {{{(0.3+0.9)/8}}} = {{{1.2/8}}} = 0.15.   Correct.

<U>Answer</U>.  The ratio of the volume of the 10% antifreeze to the volume of the 18% antifreeze must be {{{3/5}}},  or  0.6.
</pre>

Solved.


For many other solved problems on liquid mixtures see the lessons 

&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/Word-problems-on-mixtures-for-antifreeze-solutions.lesson>Word problems on mixtures for antifreeze 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/OVERVIEW-of-lesson-on-word-problems-for-mixtures.lesson>OVERVIEW of lessons on word problems for mixtures</A>

in this site.


Also, 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>.