Linear Equation Help

Discussion in 'Math' started by amilton542, Jun 28, 2012.

  1. amilton542

    Thread Starter Active Member

    Nov 13, 2010
    494
    64
    Firstly, I would just like to add, this question is not a homework problem. If I go through a book and stumble across a question I could not solve, I will always write it down and return to it at a later date (hoping I will solve it).

    Anyway, I was cleaning out my room and found a scrap piece of paper with a problem on (from a level 1 GCSE book) I remembered I could not solve, and it's still the case today.

    So here's the question:

    x g of cartridge brass (70% copper, 30% zinc, by mass) and y g of naval brass (62% copper, 37% zinc, 1% tin, by mass) when fused together give a new alloy containing 342.6g of copper and 165.6g of zinc. Find x and y.

    Answer: x = 330, y= 180.

    It's always been the 1% tin that's made the problem more ugly (maybe this is not so for others). Will someone out there please put me out my misery. Thank you.
     
  2. WBahn

    Moderator

    Mar 31, 2012
    17,788
    4,808
    Sometimes the best way to come at a problem that is giving you, well, problems is to devise a trivially simple problem that has the same essence.

    Consider this problem: I have a bunch of red buckets and black buckets. Each red bucket contains 10g of gold, 20g of silver, and 70g of assorted reddish rocks. Each black bucket contains 30g of gold and 15g of silver and 65g of coal.

    A pile is made by dumping some red buckets and some black buckets and mixing them altogether with the end result being that the pile contains 70g of gold and 50g of silver. How many buckets of each type were dumped?

    If that doesn't help, then take things step by step.

    Q1) Give x, how many grams of copper are there?
    Q2) Give x, how many grams of zinc are there?
    Q3) Give y, how many grams of copper are there?
    Q4) Give y, how many grams of zinc are there?
    Q5) Give x+y, how many grams of copper are there?
    Q6) Give x+y, how many grams of zinc are there?

    Notice how neither approach appears to give a hoot about reddish rocks, coal, or tin.
     
  3. strantor

    AAC Fanatic!

    Oct 3, 2010
    4,302
    1,988
    oowahweewah!
    I can do it. see attached.

    What's GCSE?
     
  4. amilton542

    Thread Starter Active Member

    Nov 13, 2010
    494
    64
    @ Wbhan

    The pile will require one black bucket and two red ones. The end result (what's in the pile) is all that matters. Oh well, you live and learn.

    @ Strantor

    Nice job. I'll put it in your wages.

    GCSE: General Certificate of Secondary Education
     
  5. 1chance

    Member

    Nov 26, 2011
    42
    184
    @WBahn It is ironic that you used "buckets" to solve this as when I teach this type of problem to my algebra I students, I call it the "bucket method" and we literally draw the buckets and then label the contents so you end up with bucket1 plus bucket2 equals the mixed bucket. My students have a tendancy to remember this as a good way to solve word problems which are really just systems of equations in disguise.
     
  6. WBahn

    Moderator

    Mar 31, 2012
    17,788
    4,808
    I tend to use examples that are easy to visualize, in large part because that's how I've always gone about getting my mind around problems, What amazed me was when I discovered how many people seldom, if ever, visualize anything about a problem in their mind and how many others can only do so if it is closely related to something that they have physically seen at some point.

    So when a problem says that substance A is 10% this, many people have a hard time visualizing that is a useful way, but when you say that a box of substance A is 10% this, many people that couldn't visualize the more abstract notion all of a sudden have no problem.
     
  7. debjit625

    Well-Known Member

    Apr 17, 2010
    790
    186
    I think the main problem is academics, which teaches students only the process .For me Math is a language, if you learn to describe your problems with this language you can work with it easily.

    Like in this example ,if you can describe the problem in the language of Math then it will be too easy to solve the problem...

    So it says the sum of (x) cartridge brass 70% Cu and (y) naval brass 62% Cu is 342.6 grams Cu,With the language of math we can write it like this

    Equation 1
    0.7x + 0.62y = 342.6

    Again it says the sum of (x) cartridge brass 30% Zi and (y) naval brass 37% Zi is 165.6 grams Zi. With the language of math we can write it like this

    Equation 2
    0.3x + 0.37y = 165.6

    Now we have two equations with two variables(system of linear equations with two variables) ,so we can solve that...

    Multiply 0.3 to the Equation 1 and 0.7 to the Equation 2

    Eq 1
    0.21x + 0.186y = 102.78

    Eq 2
    0.21x + 0.259y = 115.92

    Subtract Eq 1 from Eq 2

    0.073y = 13.14

    y = {13.14 \over 0.073}

    y = 180

    So y = 180,now substitute the value of y in Eq 1 to get the value of x

    0.7x + 180*0.62 = 342.6

    x = {231 \over 0.7}

    x = 330

    Good Luck
     
  8. amilton542

    Thread Starter Active Member

    Nov 13, 2010
    494
    64
    I've always found learning math is the easy part; it's trial and error. It's knowing how to apply it accordingly.

    For instance, how do you apply it to the Universe?

    "For some reason we do not yet understand, mathematics is the language of the cosmos."
     
  9. strantor

    AAC Fanatic!

    Oct 3, 2010
    4,302
    1,988
    e=mc^2
    _____
     
  10. WBahn

    Moderator

    Mar 31, 2012
    17,788
    4,808
    I agree. As you pointed out in your first post, the problem you were having wasn't with the math, it was with understanding the role (or lack thereof) of some of the given information. Had the problem been worded slighly differently, that other information would have been necessary. As it was, it was extraneous.

    Usually, the "word problem" we start from (whether it be in an academic situation or in real life) requires pulling fractions of mathematical relationships from different parts and then organizing them so as to embody the higher relationships in the problem, some of which may have to be inferred or assumed.

    But, once we have done this, I think there is real value is taking the equations that come out of it and then doing something aking to a direct translation from the math back to natural language. Doing so will often either reveal a better understanding of the problem, or reveal that we have done something wrong and our mathematical translation doesn't math the natural language one.
     
    amilton542 likes this.
  11. debjit625

    Well-Known Member

    Apr 17, 2010
    790
    186

    Obviously it could be described with math (or math could be applied to Universe), its already known this far that the Universe is govern by four fundamental laws (math equations).Gravitational force, Electromagnetic force, Strong nuclear force , Weak nuclear force.

    Today we are trying to find out one law (one master equation) that describes the whole universe...

    Till we don't find that one law, we could describe the universe by the four fundamental laws.

    Universe is too much crazy, you really need a crazy mind to understand it, for me there are many parts that I can’t visualize properly as those concept are totally abstract or may be I don’t have any concrete model to describe that ,but right now I have a little idea how these four forces are interacting with each other in some areas.
     
  12. amilton542

    Thread Starter Active Member

    Nov 13, 2010
    494
    64
    Yes, the Universe can be described by laws with respect to the greatest minds of human kind whom derived them.

    But how does one even begin to set up a model to make a prediction or even derive that law. Basically, "If these conditions hold, then the answer is yes."
     
Loading...