Question 1190210
.
A merchant wishes to mix gourmet coffee selling for $8 per pound, $10 per pound, 
and $15 per pound to get 50 pounds of a mixture that can be sold for $11.70 per pound. 
The amount of the $8 coffee must be 3 pounds more than the amount of the $10 coffee. 
Find the number of pounds of each that must be used.
~~~~~~~~~~~~~~~


<pre>
Let x be the pounds of the $10 coffee;

then $8 coffee is (x+3) pounds, and the $15 coffee is the rest (50-x-(x+3)) = (47-2x) pounds.


The combined cost of ingredients and the cost of the mixture is the same, 

so we write this equation


    10x + 8(x+3) + 15(47-2x) = 50*11.70.


Simplify and find x


    10x + 8x + 24 + 15*47 - 30x = 50*11.70

          -12x = 50*11.70 - 24 - 15*27

          -12x = -144

             x = (-144) / (-12) = 12.


<U>ANSWER</U>.  12 pounds of the $10 coffee;  12+3 = 15 pound of the $8 pounds coffee and the rest, 50-12-15 = 23 pounds of the $15 coffee.


<U>CHECK</U>.  {{{(12*10+15*8+23*15)/50}}} = 11.70 dollars per pound, the averaged price.  ! Precisely correct !
</pre>

Solved.