Question 1086441
.
The Divine Chocolate store want to create a new truffle mix that consists of milk chocolate and hazelnut. 
If hazelnuts sell for $6 per pound and milk chocolate sells for $3 per pound, how many pounds of each should they mix together 
to create a six-pound box that sells for $5 per pound? 
~~~~~~~~~~~~~~~~~~~~~


<pre>
Take x (now unknown) pounds of milk chocolate and y (now unknown) pounds of hazelnuts.


Then the total mass of the mix is x+y pounds, and your equations are

 x +  y = 6     (1)   (total mass equation in pounds)
6x + 3y = 5*6   (2)   (total value in dollars)

In other words,

 x +  y =  6,   (1)
6x + 3y = 30.   (2)


From equation (1) express x = 6 - y and substitute it into the equation (2). 
You will get a single equation for single unknown y:

6*(6-y) + 3y = 30.


Simplify and solve for y:

36 - 6y + 3y = 30,   or

-3y = 30 - 36,

-3y = -6,

y = {{{(-6)/(-3)}}} = 2.


Thus you found the unknown y. It is 2.

So you need to use 2 pounds of hazelnuts.

Then the mass of milk chocolate is 6 - 2 = 4 pounds.


<U>Answer</U>. Mix 4 pounds of milk chocolate with 2 pounds of hazelnuts.
</pre>

Solved.



There is entire bunch of 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=http://www.algebra.com/algebra/homework/word/mixtures/Solving-typical-word-problems-on-mixtures-for-dry-substances-coffee-nuts.lesson>Word problems on mixtures for dry substances like coffee beans, nuts, cashew and peanuts</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-dry-substances-like-cookies-candies.lesson>Word problems on mixtures for dry substances like candies, dried fruits</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/mixtures/Word-problems-on-mixtures-for-dry-substances-like-soil-and-sand.lesson>Word problems on mixtures for dry substances like soil and sand</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>

&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.


Read them and become an expert in solution the 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 online textbook under the topic "<U>Mixture problems</U".