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Posted on Apr 25, 2016 at 12:30 PM

A coffee puzzle:  

In honor of Diana who so loves math puzzles

 

A man running an all-night convenience store has some five dollar per pound bulk coffee and some ten dollar per pound bulk coffee. 

 

A lady wants some eight dollar per pound coffee.  So, the man says, “I just might have some in the store room.  So he goes back “to his store room and mixes some of each of the two bulk coffees he has on hand so that the mixture is worth eight dollars a pound. 

 

What fraction of a pound is each type of coffee in his mixture? 

 

 know, this problem is really too easy for folks as smart as you all.  High school algebra.  Not a trick in it.    

 

So that everyone can have the fun of solving it, post only the answer.  Not the set-up, equations, process, reasoning, and so on. 

 

I will not confirm or dispute anyone’s answers so all can do on their own. 

 

This puzzle came from an IQ test.   Wexler. 

 

 


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Posted on Apr 30, 2016 at 11:17 AM

Quoting author:

Oh RMac.....I'm afraid I would likely need some private tutoring to get it. 😔😔

 

I did pass Algebra in school, but it's just been too long ago. 



I am certain a private tutor can be arranged.  My only fear in that regard is that he will get distracted and forget all the mathematics he ever knew.  Just thinking about the prospect has already fogged his mind. 

 


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Posted on Apr 29, 2016 at 08:54 PM

Quoting author:

@ Diana

 

Re “ PS:  RMac, smoke coming out of a woman's ears is always the first sign it is time to back away...because something really bad is going to happen....and it generally happens to the man!  lolol *wink*   :))) 

  

Not in this case though.

  

Well, I am grateful for that.   

 

BTW Have you seen my sneaky solution method?  Do you understand it? 

 


Oh RMac.....I'm afraid I would likely need some private tutoring to get it. 😔😔

 

I did pass Algebra in school, but it's just been too long ago. 


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Posted on Apr 29, 2016 at 08:51 PM

Quoting author:

You got the correct answer, if the question was how much $10 coffee can you buy if you only have $8.63, 13.808 ounces.  Without doing any more calculations, it can be deduced that she can buy 27.616 ounces of $5 coffee.  We just figured out that you can buy twice as much $5 coffee versus $10 coffee regardless of how much money we have.  Ain't math great!

 

The problem that R presented, however, is a mixture problem.  How much $10 coffee do I mix with $5 coffee so that I have a pound of coffee that costs $8.

Let:

X= the amount of $10 in pounds or fractions of a pound

Y=  "        "      "    $5  "    "        "       "       "       "

... then 10(X) + 5(Y)= 8  and we know that X+Y= 1 pound or Y= 1-X so we substitute

 

and get 10(X) + 5(1-X)= 8 or

 

10X+5-5X=8 or 10X-5X= 3

 

5X=3, so X= 3/5  and since X+Y= 1, Y=2/5

 

By the way, I've seen your pictures.  Math skill is the very last thing a man has on his mind when dating you.

 



Yes I know Roc, but he asked a second question. We already determined the first question was above my IQ. 

 

Thank you for the compliment. I've worked hard to develop other skills to compensate for the lack of algebra prowess. 


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Posted on Apr 28, 2016 at 06:12 PM

@ Diana

 

Re “ PS:  RMac, smoke coming out of a woman's ears is always the first sign it is time to back away...because something really bad is going to happen....and it generally happens to the man!  lolol *wink*   :))) 

  

Not in this case though.

  

Well, I am grateful for that.   

 

BTW Have you seen my sneaky solution method?  Do you understand it? 

 


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Posted on Apr 28, 2016 at 11:01 AM

Hmmm....my brain is hurting.  Remedial math coach anyone????

 

Ok...this is my formula for the second problem:

 

$10 is to (over) 16 oz  as (=)  $8.63 is to (over) 'x' oz

 

16 x 8.63 = 10x

 

138.08 devided by 10 = x

 

13.8 oz = x 

 

13.8 oz  of coffee = $8.63

 

 

Ooops, my other answer was wrong.  I said before 12.9, but my new answer (calculater used) is now 13.8.

 

Nevertheless....I am CERTAIN this is why I can't get a boyfriend!!!  grrrrr

 

 

PS:  RMac, smoke coming out of a woman's ears is always the first sign it is time to back away...because something really bad is going to happen....and it generally happens to the man!  lolol *wink*   :))) 

Not in this case though.


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Posted on Apr 27, 2016 at 10:11 PM

Well, this blog has pretty much run its course so as promised I will show a sneaky way to solve mixture problems. 

  

On the original coffee problem we have 5 and 10 dollar per pound coffees in bulk that we want to blend  to get coffee worth 8 dollars a pound coffee.

  

Between the 5 and ten we have 5 units in this case dollars.  We are going to need to move up 3 units from 5 and down 2 units from 10.  So we use 3/5 pound of the ten dollar coffee and 2/5 pound of the 5 dollar coffee.

  

Now does this work: 

  

Well (3/5) times 10 = 6 and (2/5) times 5 = 2 which does in fact add up to 8.  

  

Also 3/5 plus 2/5 = 1

  

So we have our 8 dollar a pound coffee. 

 

 

 

To get the 8.63 dollar coffee we had to use pennies as our fundamental unit and there were 500 of them between 5 dollars and 10 dollars.  But you get the idea. 

 


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Posted on Apr 27, 2016 at 09:38 PM

Quoting author:

Ok you two smarty pants!!  It's been over an hour and my nerves are about to melt. Smoke started to come out of my ears at about 30 minutes. 😖

 

If it were me, I'd just give her 12.8 oz of the $10/lb coffee for $8, but that doesn't answer the question properly. Drat!!!

 



Which two smarty pants are you referring to?  roc and Z?  roc and me?  me and Z? 

 

The smoke test generally means the part of the circuitry has burned out.  

 

I will teach you a sneaky way to solve two variable problems in a few days after a few more people chime in. 

 

Hope you feel better tomorrow. 

 

Thanks


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Posted on Apr 26, 2016 at 09:38 PM

Quoting author:

60/ 40%


The 60% is of which coffee?  And the 40%?  

 

Hey, it is good to see you.  Thanks


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Posted on Apr 26, 2016 at 08:01 PM

Quoting author:

Suppose the lady had asked for coffee that cost 8 dollars and 63 cents.  She robbed the baby’s piggy bank and wanted to get the best coffee she could with the amount of money she had.  Answers preferred in the form of rational numbers such as 432/500.  Not a correct answer by the way. 


I know, if you could solve the first version you can solve this one.   

 



12.9 (13oz) of $10/lb coffee for the second question. 


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Posted on Apr 26, 2016 at 07:26 PM

Ok you two smarty pants!!  It's been over an hour and my nerves are about to melt. Smoke started to come out of my ears at about 30 minutes. 😖

 

If it were me, I'd just give her 12.8 oz of the $10/lb coffee for $8, but that doesn't answer the question properly. Drat!!!

 


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Posted on Apr 26, 2016 at 06:48 PM

Suppose the lady had asked for coffee that cost 8 dollars and 63 cents.  She robbed the baby’s piggy bank and wanted to get the best coffee she could with the amount of money she had.  Answers preferred in the form of rational numbers such as 432/500.  Not a correct answer by the way. 


I know, if you could solve the first version you can solve this one.   

 


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Posted on Apr 26, 2016 at 06:38 PM

Quoting author:

... I just don't want Diana to hurt herself so I'll just jump in here.

 

In a perfect world...

 

3/5ths of a pound of the $10 coffee plus 2/5ths of a pound of the $5 coffee.

 

..... but, if Trump wins, we'll all have to switch to English Tea since no coffee will be able to get over, under or around the wall.

..... if Bernie wins, coffee will be free

....  if Cruz wins, the Supreme Court will have to rule whether the right to drink coffee is guaranteed in the  Constitution

... and if Hillary wins, all bets are off.  Quantities will be limited and only available from her private server.  A Congessional investigation will be convened,


Bless you for your kind concern re Diana.  We would not want any harm to befall her. 


As long as my free coffee is not that cat poop coffee I'm good. 


Another reason not to vote for Trump. 


Re Hilary, if that is my only coffee choice I may have to swicth to that other guy.  Not Cruz, you know, that other guy. 


 

I had not thought of the political implications.  Thanks

 

 


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Posted on Apr 26, 2016 at 09:01 AM

60/ 40%


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