Any math whizzes in the house?

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Tonyd0821

Banned
o.k. i was originally going to PM Calesta this math problem, due to the fact i know he is good with it. BUT, i then thought of the fact that some people actually like doing math. (im not one of them)

My little brother emailed me with a intermediate algebra problem.
i received a "c" in algebra and for the life of me, i cannot figure out how to set up the equation for this problem. i remember how to solve equations, but i am no good at setting them up....

So, i decided to post it on here, and if you like doing math, then eat your little heart out. also, can you give an explanation as to why you set up the equation the way you did?


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Suppose that you have a supply of a 30% solution of alcohol and a 70% solution of alcohol. How many quarts of each should be mixed to produce 20 quarts that is 40% alcohol.

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and before you flame me because this is a "easy problem"
i majored in English and could write you a paper that would
be worthy of a Pulitzer :p ....
but i suck at math.

My original answer to mike (my brother) was kill the (.3 and .7 which represent percentages) DECIMALS <EDIT>>by multiplying by 10.
so:

(30x)+(70x)=40(20)

which obviously was wrong. i dont think 30 and 70 can share the same variable?
 
Originally posted by Calesta@Sep 11 2003, 03:26 PM
Ok, more like 20 seconds. :lol:

Want the explanation or should I wait?
Click to expand...

explanation please !!!

i even had my gf who is a math whiz as well work on it. (obviously not as good as you guys)

i just think it is the fact i have never dealt with mixtures and what not. so the problem is a tad unfamiliar to me...
 
Ok, this is the "cheap" way that I did it:

s3f60db1341ed5.jpg


The one highlighted box that shows you the formula is the only formula you need to use. Varying the three values on the first row would allow you to use any percentages and any total volume you want.

I'll give you the proper algebraic way to solve it (without a spreadsheet) as soon as I edit a user...
 
Damn...makes me realize how much I've lost in math...French Scientific Baccalaureate and I can't remember shit...
 
the correct ratio is 1.66qts 30% solution to 1qt 70% yielding 2&2/3qts 40% solution

not complete burt I did it in my head
 
fucking amazing.....

but how should i explain for him to do it on a scientific calculator?


and the answer is .3(15)+.7(5)=.4(20) but i cant figure out how to set up the equation to get 15,5....

3x+7x?
 
:p

You = BA type person. :)

Makes me realize how much I've lost that I flipped open Excel to do it before just writing down an equation or two and solving.

:eek:
 
Originally posted by Calesta@Sep 11 2003, 03:30 PM
Ok, this is the "cheap" way that I did it:

s3f60db1341ed5.jpg


The one highlighted box that shows you the formula is the only formula you need to use. Varying the three values on the first row would allow you to use any percentages and any total volume you want.

I'll give you the proper algebraic way to solve it (without a spreadsheet) as soon as I edit a user...
Click to expand...

edit a user? u mean correct someone who gives a wrong answer?
 
Originally posted by Calesta@Sep 11 2003, 03:33 PM
:p

You = BA type person. :)

Makes me realize how much I've lost that I flipped open Excel to do it before just writing down an equation or two and solving.

:eek:
Click to expand...

BA?

bad algebra? :lol:

bachelor sp... of arts?
 
Here's the LONG way to do it:

Let's set up two arbitrary variables... one for the 30% mix, and one for the 70% mix.

x = 1 quart of 30%
y = 1 quart of 70%

How do you find out the overall percentage of the final mix? You add up the total amount of alcohol, then divide by the overall total volume.

First, let's find the overall total amount of alcohol:

.3x + .7y = total quarts of alcohol

To find the total percentage, just divide the total amount by the total volume. You have 20 quarts total, so divide by that to get your percentage:

(.3x + .7y) / 20 = total (or final) percentage of alcohol)

You want your final percentage to be 40%, right? Set everything on the right side of the equal sign to .4.

(.3x + .7y) / 20 = .4

That's the equation we'll be working with.

Now you have two variables, and you only have one equation... what do you do? You can't solve for two vars with one simple equation. Simple, let's just remove one. What's the relationship between x and y? They both must add up to 20.

So... y = 20 - x.

Substitute for y, and you get:

(.3x + .7(20 - x)) / 20 = .4

Simplify (I'll do this step by step too):

(.3x + 14 - .7x) / 20 = .4

(14 - .4x) / 20 = .4

14 - .4x = 8

-.4x = -6

x = -6 / -.4

x = 15

Since we found before that y = 20 - x, we get y = 5.

You need 15 quarts of 30% alcohol and 5 quarts of 70% alcohol to get a final solution of 20 quarts of 40% alcohol.

Easy.

:lol:

Do it fast in a spreadsheet and you can vary for any type of final mixture, based on any kind of input fluid.
 
Originally posted by Calesta@Sep 11 2003, 03:46 PM
Here's the LONG way to do it:

Let's set up two arbitrary variables... one for the 30% mix, and one for the 70% mix.

x = 1 quart of 30%
y = 1 quart of 70%

How do you find out the overall percentage of the final mix? You add up the total amount of alcohol, then divide by the overall total volume.

First, let's find the overall total amount of alcohol:

.3x + .7y = total quarts of alcohol

To find the total percentage, just divide the total amount by the total volume. You have 20 quarts total, so divide by that to get your percentage:

(.3x + .7y) / 20 = total (or final) percentage of alcohol)

You want your final percentage to be 40%, right? Set everything on the right side of the equal sign to .4.

(.3x + .7y) / 20 = .4

That's the equation we'll be working with.

Now you have two variables, and you only have one equation... what do you do? You can't solve for two vars with one simple equation. Simple, let's just remove one. What's the relationship between x and y? They both must add up to 20.

So... y = 20 - x.

Substitute for y, and you get:

(.3x + .7(20 - x)) / 20 = .4

Simplify (I'll do this step by step too):

(.3x + 14 - .7x) / 20 = .4

(14 - .4x) / 20 = .4

14 - .4x = 8

-.4x = -6

x = -6 / -.4

x = 15

Since we found before that y = 20 - x, we get y = 5.

You need 15 quarts of 30% alcohol and 5 quarts of 70% alcohol to get a final solution of 20 quarts of 40% alcohol.

Easy.

:lol:

Do it fast in a spreadsheet and you can vary for any type of final mixture, based on any kind of input fluid.
Click to expand...

....next time you need a letter or papaer written, lemme know :lol:

thanks Cal.

i knew i was almost there....but something was amiss....
 
BA = Bachelor of Arts. :)

OR

You can do this the intuitive way...

If you just do half and half (10 and 10) you'll end up with a percentage square in the middle... (50%). Just go halfway again "toward" the lower percentage, and add 5 more quarts to 30% and take 5 away from 70% to get 40%. That would have your answer in about... 2 seconds.

:lol:
 
Originally posted by Tonyd0821@Sep 11 2003, 03:49 PM
....next time you need a letter or papaer written, lemme know :lol:

thanks Cal.

i knew i was almost there....but something was amiss....
Click to expand...

I'll let you take the verbal portion of the GRE for me, how's that? :lol:

I think it would be easier for Katie to take care of that... and no worries there for me either- I'm not too bad at writing papers, especially when I only have to write about technical stuff and research. There's no flair there- just cold hard facts reporting and a need to be as concise as possible.

:)
 
Originally posted by Calesta+Sep 11 2003, 03:51 PM-->
Calesta @ Sep 11 2003 said:
Tonyd0821
Click to expand...
Calesta @ Sep 11 2003 said:
@Sep 11 2003, 03:49 PM
....next time you need a letter or papaer written, lemme know :lol:

thanks Cal.

i knew i was almost there....but something was amiss....
Click to expand...

I'll let you take the verbal portion of the GRE for me, how's that? :lol:

I think it would be easier for Katie to take care of that... and no worries there for me either- I'm not too bad at writing papers, especially when I only have to write about technical stuff and research. There's no flair there- just cold hard facts reporting and a need to be as concise as possible.

:)
Click to expand...

verbal rocks !!!!

im more into the "argumentative" type of writing. I think it is so much fun to sit down and try and convince someone of your point of view. fallacies can be your worst enemy in that type of writing situation, so you must walk a very thin line in terms of how you present your side. fun fun fun. :lol:

only thing i hate is the research. bah.
 
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