Question 1149256
.
In what ratio must two sorts of {{{highlight(cross(suger))}}} <U>sugar</U>, costing $390 and $315 per kg respectively, 
be mixed in order to produce a mixture worth $345 {{{highlight(per_kg)}}} <U>?</U>
~~~~~~~~~~~~~~


<pre>
Let x be the mass of the $390 sugar and y be the mass of $315 sugar.


We want to find the ratio {{{x/y}}}.


Your basic equation is


    390x + 315y = 345*(x+y).     (1)


Why the equation has this form, is absolutely clear, and I will not explain it further.


Since we want to know the ratio  {{{x/y}}},  divide equation  (1) by "y" (both sides). You will get


    {{{390*(x/y)}}} + 315 = {{{345*((x/y) + 1)}}}.     (2)


For simplicity, denote  {{{x/y}}} as z; then  equation (2) takes the form


    390*z + 315 = 345*z + 345.


Simplify and find z


    390z - 345z = 345 - 315

    45z = 30

      z = {{{30/45}}} = {{{2/3}}}.


<U>ANSWER</U>.  The ratio  {{{x/y}}}  is  {{{2/3}}}.


         In other words,  2 masses of the $390 sugar should be mixed with  3 masses of the  $315 sugar.


<U>CHECK</U>.   {{{(2*390+3*315)/(2+3)}}} = 345 dollars.   ! Precisely correct !
</pre>

Solved.


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


There is a bunch of introductory lessons in this site, &nbsp;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>


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 the 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 online textbook 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.