SOLUTION: The coffee merchant wants to blend a mildly strong coffee called Nervous Nellie with an extremely strong coffee called Nervous Breakdown to create a medium strength coffee he plans

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Question 740890: The coffee merchant wants to blend a mildly strong coffee called Nervous Nellie with an extremely strong coffee called Nervous Breakdown to create a medium strength coffee he plans to call Nervous Wreck. If the Nellie flavor costs $1.20 per pound and the Breakdown flavor costs $1.40 per pound, how many pounds of the Nellie is needed to create a 30 pound blend which costs $1.35 per pound?
Found 3 solutions by lynnlo, ikleyn, greenestamps:
Answer by lynnlo(4176) About Me  (Show Source):
You can put this solution on YOUR website!
4 1/2 pounds

Answer by ikleyn(53418) About Me  (Show Source):
You can put this solution on YOUR website!
.
The coffee merchant wants to blend a mildly strong coffee called Nervous Nellie with an extremely strong coffee called Nervous Breakdown to create
a medium strength coffee he plans to call Nervous Wreck. If the Nellie flavor costs $1.20 per pound and the Breakdown flavor costs $1.40 per pound,
how many pounds of the Nellie is needed to create a 30 pound blend which costs $1.35 per pound?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

Let x be the number of pounds of the $1.20 per pound coffee (Nellie).

Then the number of pounds of the $1.40 per pound coffee (Breakdown) is (30-x).


Write the total money equation

    1.20x + 1.40(30-x) = 30*1.35  dollars.


Simplify and find x

    1.20x + 1.40*30 - 1.40x = 30*1.35

     -0.2x = 30*1.35 - 30*1.40

     -0.2x = 30*(1.35-1.40)

     -0.2x = 30*(-0.05)

     0.2x = 30*0.05

        x = 1.5%2F0.2 = 15%2F2 = 7.5 pounds.


ANSWER.  7.5 pounds of the Nellie coffee is needed.


CHECK.   %281.20%2A7.5+%2B+1.40%2A%2830-7.5%29%29%2F30 = 1.35 dollars per pound, the price for the pound of the blend.  ! correct !

Solved.

The answer 4 1/2 pounds in the post by @lynnlo is incorrect.



Answer by greenestamps(13258) About Me  (Show Source):
You can put this solution on YOUR website!


The response from tutor @ikleyn shows a standard formal algebraic solution for mixture problems like this.

You can also solve this or any similar mixture problem using the idea of weighted averages; the problem can be solved quickly with simple mental arithmetic if the numbers in the problem are "nice".

In this problem the price per pound of the mixture is 3/4 of the way from the lower price to the higher price; that means 3/4 of the mixture must be the more expensive ingredient.

3/4 of 30 pounds is 22.5 pounds, so the mixture must contain 22.5 pounds of the Breakdown flavor, which means 30-22.5 = 7.5 pounds of the Nellie flavor.

ANSWER: 7.5 pounds