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 740885: 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?
Please include how you got the solution
Found 4 solutions by lynnlo, ikleyn, greenestamps, timofer:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by ikleyn(53419) 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 7 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 the other tutor shows a solution using the standard formal algebraic method for solving this mixture problem.

For any 2-part mixture problem like this one, the problem can be solved informally by a different method; in this problem the solution by this alternative method is very quick and easy because the numbers are "nice".

The short, quick, and easy solution....

Because $1.35 is three-fourths of the way from $1.20 to $1.40, 3/4 of the mixture must be the more expensive flavor. 3/4 of 30 pounds is 22.5 pounds.

ANSWER: 22.5 pounds of the Breakdown flavor, so 30-22.5 = 7.5 pounds of the Nellie flavor

Answer by timofer(136) About Me  (Show Source):
You can put this solution on YOUR website!
---------------------------------------------------------------
                price          pounds          costs
---------------------------------------------------------------
nellie           1.2             30-c          1.2(30-c)
breakdown        1.4               c           1.4c
wreck(blend)     1.35            30            1.2(30-c)+1.4
----------------------------------------------------------------

To account for cost 1.35%2A30=1.2%2830-c%29%2B1.4c
1.35%2A30=36-1.2c%2B1.4c
1.35%2A30=36%2B0.2c
c=%281.35%2A30-36%29%2F0.2

c=22.5, the pounds of Breakdown
which means 7.5, the pounds of Nellie