Question 1092927
.
<pre>
Let x = # teaspoons of the 10% HR;
    y = # teaspoons of the 60% HR.

Then the system of equations is 

   x +     y = 4,        (1)     (total volume, in teaspoons)
0.1x + 0.60y = 0.55*4    (2)     (the pure HR contents)

 
Multiply the second eqn by 100 to get

   x +     y = 4,        (1')    
 10x +   60y = 220       (2')


Express x = 4 - y from (1), and then substitute into (2'). You will get

10*(4-y) + 60y = 220.

40 - 10y + 60y = 220,  ====>  50y = 220 - 40 = 180  ====>  y = {{{180/50}}} = {{{3}}} {{{3/5}}}.
</pre>

<U>Answer</U>.  {{{3}}} {{{3/5}}} teaspoons of the 60% HR and {{{2/5}}} teaspoons of the 10% HR.



It is a typical mixture word problem.


There is entire bunch of introductory lessons covering various types of mixture problems

&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/Word-problems-on-mixtures-for-alloys.lesson>Word problems on mixtures for alloys</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.


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

&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>".