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Help me with math?
    #12918692 -

*If I don't get a great response here I will post in the pub. Math seems science/tech related though.

So I'm somewhat embarrassed to be posting this, but my math really is piss poor and I need help.

I quit taking math about eight years ago in high school, and never looked back.
Recently I enrolled in a professional brewing program, and am working towards my master brewers certificate.

This is the final week of my prep course, and I have finished all the chapters except the calculations chapter, which has me completely stumped.

I finished all the chemistry and biology without trouble, but math is the kind of thing I really need to be spoon-fed to understand properly.

Seems like it is all basic algebra, so I'm pretty embarrassed that I can't do it. I only have six questions left and then I'm finished my course.

I'll give you the first problem and post the rest when I get to them.

The first problem is a mixing formula.

Aa+Bb=Cc

Where A, B, and C are volumes of liquid, and a, b, and c are characteristics of those liquids. For instance 5% alcohol, 10% caustic solution, 15degrees Celsius, etc.

When we need to determine the liquid volume of C, and the characteristic(temperature, causticity, alcohol) of c, I can do the questions. However something funny happens in the problem I am stuck on.

Here is the example from the course material.

We are trying to figure out how much 30% caustic to add to our 3% caustic solution to get a final concentration of 4% caustic.

All volume measures are in hectoliters.

So:

A = 200HL a = 3% causticity B = ? b = 30% causticity C = 200+B c = 4%

(200)(3)+(B)(30)=(200+B)(4)  so far so good.
600+30B = 800 +4B            still got it.
30B-4B = 800-600            almost totally lost.
26B = 200                    makes sense again
B = 200/26                  simple
B = 7.69       

So we should add 7.69 hectoliters of 30% caustic to our solution, to reach a final causticity of 4%.

So it's mostly the third step that is really throwing me.

I know I should probably know this stuff, because it's high school level algebra, but I really need help.

I'll post the next problem when I get this one figured out.


--------------------
I am the king of Rome, and above grammar! - Emperor Sigismund

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Re: Help me with math? [Re: Heffy]
    #12918726 -

On the third step you have to do the same thing to both sides to isolate B.  In the second step you have a B on each side - thats not what you want.  You move the B over by subtracting 4B from each side.  Now you have all the Bs on the left.  But there are still non-Bs on the left, the 600 term.  You have to move it to the right by subtracting 600 from each side.  After doing these two steps you have moved all your B terms to the left and all your non-B terms to the right.

Another thing I notice is that 3% is not 3, its .03.

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Re: Help me with math? [Re: ModusPwnd]
    #12918754 -

Thanks for replying.

So here is the actual question.

(10)(2)+(B)(40)=(20+B)(4)
20+40B=80+4B
40B-4B=80-20
36B=60
B=1.66666

So we should add 1.66666 HL of 40% caustic to reach our 4% causticity solution.

Have I done this correctly?

Note: since we are trying to define the value of B I don't think the decimal place really affects the answer. You are right though technically the equation should look like:
(10)(.02)+(B)(.40)=(20+b)(.04)
Although I think it would still call for 1.6666HL in the answer.


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I am the king of Rome, and above grammar! - Emperor Sigismund

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Re: Help me with math? [Re: Heffy]
    #12918854 -

I haven't done math in about 2 years but I went up to calc 2 in college.  I'm sure they gave you a couple of examples.  I got the same results though. 

The formula is working for now because your making the same mistake on both sides.  I wouldn't get in the habit though if you ever try to make something high gravity in the future.


--------------------
The butcher with the sharpest knife has the warmest heart.

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Re: Help me with math? [Re: dickpayne00]
    #12918982 -

So I made it through the next 2 questions by myself.

Only 3 more questions to go, and then I can celebrate :volcano:  :guinness:


Here is the next problem.

BHE% = Brew House Efficiency
Y = kg extract in malt
Z = kg malt

BHE% = kg extract in wort x 100/kg extract in malt = hot wort vol(L) x 0.96 x gravity% x 100/kg malt x extract fine grind%

note: my gravity in this brew is 1.0611. I am not sure how they want me to put this in as a percentage, so I'm just putting it in as is.

BHE% = 954.6 x 100/Y = 60 x 0.96 x 1.0611 x 100/Z x 0.78

BHE% = 95,460/Y = 6,111.936/Z x 0.78

At this point am unsure how to proceed.

Need to know the value of Z to complete problem, and proceed with other problems. All of the last few problems are using the same figures, so I can't go on until I can define the value for Z.

Thanks for helping. This place really is great.


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I am the king of Rome, and above grammar! - Emperor Sigismund

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Re: Help me with math? [Re: Heffy]
    #12919501 -

Think I've mostly got it.

BHE% = (954.6)(100)/1223.8 = (60)(o.96)(15.91)(100)/(Z)(o.78)

= 95460/1223.8 = 91641.6/(Z)(o.78)

= 78.0029 = 91641/(Z)(o.78)

= 60.842 = 71,479.98Z

Z = 1,174.84599

Can anyone tell me if I've made any glaring mathematical errors? I'm almost positive I have. I shouldn't be ending up with a number that is lower than 1223.8

Help?


--------------------
I am the king of Rome, and above grammar! - Emperor Sigismund

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Re: Help me with math? [Re: Heffy]
    #12919601 -

Is your 0.78 supposed to be in the numerator or denominator?

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Re: Help me with math? [Re: ModusPwnd]
    #12919779 -

I multiplied both figures in the third column.

If I divide I get:


= 100.003718 = 117,488.462Z

= 1,174.84

Same answer.

I think I am doing something wrong.

I am hopeless when it comes to math.
:facepalm:
I wish they spent more time reviewing the algebra.


--------------------
I am the king of Rome, and above grammar! - Emperor Sigismund

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Re: Help me with math? [Re: Heffy]
    #12919960 -

I think I've finally input all the data correctly and worked the equation out correctly.

If I am still making a mistake hopefully someone can catch it before I hand my work in.

(954.6)(100)/1223.3 = (6000)(0.96)(.1591)(100)/(Z)(o.78)

= 95,460/1223.3 = (91,641.6)(Z)(0.78)

= 78.034 = (91,641.6)(Z)(0.78)

= (78.034)(0.78) = (91,461.6)(0.78)(Z)

= 60.866 = 71,340.048Z

Z = 1,172.083

: you would need 1172 kg of malt, to make 6000 liters of beer, at 96% efficiency, with a gravity of 1.0611


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I am the king of Rome, and above grammar! - Emperor Sigismund

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