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Surgeon General Warning! This algebra problem may kill you or someone you love.


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I have discovered the lethal algebra problem, the one that will make you either kill your 13 year old son, or make him kill you, or possibly a joint suicide pact in order to get algebra over with once and for all!

 

Yep, this one...this completely lethal, Ebola Virus laden, Anthrax mutated, nuclear problem is definitely the ultimate weapon of mass destruction. I am sure the department of Homeland Security must get involved and eradicate this problem from every math book in America lest this generation of youth become extinct.

 

Here it is:

 

How many liters of a 60% acid solution must be added to a 75% solution to create 20 liters of a 72% solution?

 

That's the problem. Now, I have allowed ds to live...he is fuming in the corner at the evils of the math industry in collusion with the pharmaceutical industry and trust me, YOU DON'T WANT MY DS TO BE YOUR PHARMACIST!!!!!! His personal philosophy on drug manufacturing being, well if a little bit is good, a whole lot must be quite a bit better, and who needs to know what dilution means????

 

Ds has allowed me to live and DH did not have to physically restrain either of us. I am hiding in my room with an atomic mug of coffee. Ds is eating potato chips. At some point before we go see Voyage of the Dawn Treader this evening, we will have to make up but if we do manage to, I think it should be filmed and sent to North and South Korea..."See, if they can do it, so can you!!"

 

4 years 8 months until college, 4 yrs. 8 mths. until college, 4 yrs. 8 mths. until college.....

 

I'm going to be a basket case by then; I just know it!

 

Faith

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Yeah, we have some of those lethal math problems around here, too (if you saw my recent thread).

 

FTR, I hate those mixing dilution problems, too. I try to get along with math, but really - as I'm not a pharmacist, I couldn't care less what the proper dilution should be. :tongue_smilie:

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Here's how you solve it.

 

You know that you're going to end up with 20 gallons.

 

Let's call the amount of 60% added X.

 

That makes the original amount of 75% equal 20-X

 

Use this formula

 

(Conc1 * V1) + (Conc2 * V2) = (Conc3*V3)

 

Based on our assumptions above, we have the following

 

Conc1 = 0.75

V1 = 20-X

Conc2 = 0.60

V2 = X

Conc3 = 0.72

V3 = 20

 

Plugging all of this in gives us.

 

(0.75*(20-X))+(0.60*X)=(0.72*20)

 

Which reduces to

 

15 - 0.75X + 0.6X = 14.4

 

Which further reduces to

 

0.6 = 0.15X

 

Which further reduces to

 

4 = X

 

So you need to add 4 liters of 60% to 16 liters of 75% to get 20 liters of 72%

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We had the best day of Algebra today that we've had since November. The trick was doing every problem with him---- he's better at it than I am and loves to compete. Best he compete with me than himself or the answer book.

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I'm no math wiz, but it seems you two gave different answers...

 

 

I may be wrong, but that's how I would work it if it were given to me.

 

For 20 gallons of 72% solution, you need to end up with 14.4 liters of pure acid mixed with 5.6 liters of pure water or whatever liquid you're mixing it with.

 

4 liters of 60% solution will have 2.4 liters of acid

16 liters of 75% solution will have 12 liters of acid

 

As such, you will end up with 14.4 liters of acid by mixing these and a total volume of 20 liters.

 

This all assumes that your mixtures are by volume of course.

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Hi Dad of 4,

 

Your answer is correct and it is how I would solve it as well. I wrote out the post and then didn't get back for awhile to give the solution because ds was really, really upset and we just needed to settle and make up. Truly, his attitude stinks. But, I've come to a conclusion today. We had a long talk and I feel that ds is just not mature enough yet. There, I said it, he's just not ready.

 

His arithmetic is excellent and he's highly accurate. But his ability to think abstractly is just not as highly developed as his sister's was at this age or his 12 year old brother's is now. So, dh and I have decided to do another round of "getting ready" math plus some introductory logic and hope that in the fall, he's better able to handle the material.

 

It's actually a load off to have come to this conclusion. I can't have him dreading math every single day and getting teary eyed before starting and I can't feel my blood pressure rising just knowing it's time for our daily, "kill each other over algebra" session. Something has to give.

 

Faith

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So you need to add 4 liters of 60% to 16 liters of 75% to get 20 liters of 72%

 

I'm glad *someone* at my house knows this! ;)

 

But, I've come to a conclusion today. We had a long talk and I feel that ds is just not mature enough yet. There, I said it, he's just not ready.

 

That sounds very wise, Faith!

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Here's how you solve it.

 

You know that you're going to end up with 20 gallons.

 

Let's call the amount of 60% added X.

 

That makes the original amount of 75% equal 20-X

 

Use this formula

 

(Conc1 * V1) + (Conc2 * V2) = (Conc3*V3)

 

Based on our assumptions above, we have the following

 

Conc1 = 0.75

V1 = 20-X

Conc2 = 0.60

V2 = X

Conc3 = 0.72

V3 = 20

 

Plugging all of this in gives us.

 

(0.75*(20-X))+(0.60*X)=(0.72*20)

 

Which reduces to

 

15 - 0.75X + 0.6X = 14.4

 

Which further reduces to

 

0.6 = 0.15X

 

Which further reduces to

 

4 = X

 

So you need to add 4 liters of 60% to 16 liters of 75% to get 20 liters of 72%

 

 

My kids are soooo scr3wed.

 

This is the kind of cr4p that caused me to flunk out of Nursing School.

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. We had a long talk and I feel that ds is just not mature enough yet. There, I said it, he's just not ready.

 

It's actually a load off to have come to this conclusion. I can't have him dreading math every single day and getting teary eyed before starting and I can't feel my blood pressure rising just knowing it's time for our daily, "kill each other over algebra" session. Something has to give.

 

 

Faith, this is the conclusion I came to with my dd9 and her math (not Algebra!). At this point, I'm not sure she'll make it until age 13.

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Jean, I SOOOOOOO wish you lived nearby. I'd invite you to accompany me to Barnes and Nobles for coffee, Godiva Chocolate cheesecake, and commiseration!

 

I think I may need therapy by the time I get this child through, though admittedly it is really just math that is the nightmare. His English, History, Science, Latin, and early Logic studies are all good and his writing skills are advanced for his age and maturity level. Of course, it's no help that DH, THE LOVER OF ALL THINGS MATH, cannot relate to this child. I have to be careful to keep him out of the room when I am teaching ds because his googly-eyed, "ISN'T MATH DIVINE" mood, makes ds go nuts. It is incomprehensible to dh that he has genetically contributed to an individual who does not love math with the ardor of Cassanova!!

 

I never loved math, but I was always good at it. So, his lack of self-confidence is a new thing for us. But, he's our precious boy (I had to get out a baby picture of him today to remind me just how adorable he once was) and we'll do what's best even if it makes my face tic and his father feel forlorn.

 

I'm going to purchase Life of Fred Pre-algebra with biology and the second book with economics from Rainbow Resource. We won't bother with the biology because he's already doing Apologia physical science and much of what is in the biology was covered in the general science last year and his life sciences/zoology in 6th grade. But, he does like money and all things to do with money, theories of money, etc. It will be interesting to see if he takes an interest in the economics.

 

Faith

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Just reading this question made me nauseous and caused me extreme anxiety.

 

I started back to college about 2 years ago, and had to take the pre-algebra courses before I could get to College Algebra I. After taking the two pre-courses I needed, I started homeschooling and had to put MY school on hold for awhile. Now, I don't see how I can take College Algebra I because I have forgotten everything from those two classes!

 

I am planning on spending the summer going over the algebra books again to relearn what I forgot. But the whole thing is a huge stress issue for me!

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I know you've already found the answer here, but just wanted to mention -- we were doing these types of problems not long ago, and found the Khan Academy videos very helpful. On the link provided, look down to the heading of "Algebra I Worked Examples," and go to the second column where you'll see "Mixture Problems 1," "Mixture Problems 2," and "Mixture Problems 3." Looking at them again, I wonder if #2 and #3 will be most helpful for you. I had my dd work the Khan Academy examples, and the way he made a table for the problems was very helpful for her in setting them up.

 

HTH! And good luck with the peacemaking!

 

http://www.khanacademy.org/

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