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#1 Nitewalkr  Icon User is offline

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Differentiating between two Math questions.

Posted 02 April 2012 - 08:57 PM

Greetings;

I was told that this is the right place to ask Math questions. As you can see that i have rep 2 in negative and I hope this does not affect how people will respond to my threads.

I have a question related to the General School Level Maths. I know that I have done these but it was a very long time ago, yet now I realized that I should practice them from time to time to keep them live in memory.

There are two questions that I need to (Noobly Re-understand) to differentiate. As I read them they pretty much sound the same but they really arent.

Do not Google this to find a difference I want to understand through a discussion about how they are different so I can use a set of formula(s) in the appropriate equation(s).

1) The Length of the shadow of a flagpole was found to be 72 feet. The shadow of a 3 foot picket fence in line with the flagpole was 4 feet. What is the hight of the flagpole.

2) If 6 men can do a piece of work in 14 days, how many men are needed to do the work in 21 days?

Thanks.

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Replies To: Differentiating between two Math questions.

#2 e_i_pi  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 09:06 PM

They're both similar, but the first question is about divisive comparisons, and the second question is about multiplicative comparisons.

Basically, the first question is about this concept:
    Length of flagpole         Length of fence
------------------------- = ----------------------
Length of flagpole shadow   Length of fence shadow


...or in other words, the ratio of height to length will always be equal.

And the second question is about this concept:
6 men * 14 days = ? men * 21 days


...or in other words, the amount of man-hours of work that needs to be done is equal.

This post has been edited by e_i_pi: 02 April 2012 - 09:08 PM

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#3 Nitewalkr  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 09:18 PM

so by your definition:

1) x / 72 = 3 / 4
=> 4x = 216 = x = 54

where as:

2) 6 * 14 = x *21
=> 84 = 21x
=> 84/21 = x
=> 4 = x or x = 4

hmm, can not use a Unity method in both? Or are there different types of Unity methods.

EDIT: It kind of freaked me out when I had 9 the first time than 4 than 9 again.

EDIT 2: So if I am to be asked about a certain lengths or "number of total miles for certain hours," given that there are three known things. (anything to do with the length or a distance.) I have to use a unity method and if I am asked about the (how many people will finish this project in the stated time) I should not use the Unity method? Or just write it as it is and figure out from there?

This post has been edited by Nitewalkr: 02 April 2012 - 09:24 PM

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#4 e_i_pi  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 09:23 PM

I'm not sure what you mean by Unity methods.

You can rewrite the second question as:
  x     6
 --- = ---
  14    21


...which makes it identical to the first question in practice, but that equation is not a straight-forward interpretation of the question's wording, if you understand me.
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#5 Nitewalkr  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 09:35 PM

*Removed*

This post has been edited by Nitewalkr: 02 April 2012 - 11:29 PM

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#6 Nitewalkr  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 09:48 PM

View Poste_i_pi, on 02 April 2012 - 09:23 PM, said:

I'm not sure what you mean by Unity methods.

You can rewrite the second question as:
  x     6
 --- = ---
  14    21


...which makes it identical to the first question in practice, but that equation is not a straight-forward interpretation of the question's wording, if you understand me.


EDIT: You mean to say that set of x comes before the equal sign by any means in these word problems?

This post has been edited by Nitewalkr: 02 April 2012 - 09:49 PM

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#7 e_i_pi  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 11:47 PM

I'm not sure I'm understanding you. x can go on either side of the equation, I usually write it on the left-hand side since we read left-to-right. Is that what you're referring to?
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#8 Nitewalkr  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 02 April 2012 - 11:55 PM

View Poste_i_pi, on 02 April 2012 - 11:47 PM, said:

I'm not sure I'm understanding you. x can go on either side of the equation, I usually write it on the left-hand side since we read left-to-right. Is that what you're referring to?


No, its just that if you put the equation like this:

x / 21 = 6/14 or 6/14 = x/21 the answer comes nine. Where as, if you look at the first one we practically did just that and the answer was correct. For this one however, the answer is wrong.

If you can understand what I mean.

If you put number of men at the top and days of work at the bottom this equation would turn out be similar to yours.

Means, number of men are 'x' and 6 ; number of days of work are 14 and 21. There fore;

 x       6
---- =  ----
 14      21


Which is 4

How I did it was;

6x14 = 84

84 days per men
84/2 = 42 days ; 2 men
42/2 = 21 days ; 2+2 = 4 men

Sorry I am just trying to understand all this and trying to find a common ground between all these equations which are similar, but they actually are not. Like if I use a technique in the first question I might not be able to do it in the second.

This post has been edited by Nitewalkr: 03 April 2012 - 12:06 AM

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#9 e_i_pi  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 03 April 2012 - 12:38 AM

Look at my first post...
    6m * 14d = xm * 21d
so...
=>  6m * 14d / 21d = xm
=>  6m / 21d = xm / 14d


That's what I mean about rewriting the equation from it's original interpretation to a form that is identical to question #1.
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#10 Nitewalkr  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 03 April 2012 - 12:54 AM

View Poste_i_pi, on 03 April 2012 - 12:38 AM, said:

Look at my first post...
    6m * 14d = xm * 21d
so...
=>  6m * 14d / 21d = xm
=>  6m / 21d = xm / 14d


That's what I mean about rewriting the equation from it's original interpretation to a form that is identical to question #1.


ok, thanks. So;

 
=> 6 men in 14 days ; x men in 21 days.
=> 6m * 14d = xm * 21d

 6 men         x men
-------    =  --------
 21 days      14 days


I think I am starting to get that. I understood your first post, the second question as this was kind of confusing to me.

I'll try doing made up questions of these, is it possible to post more solved equations here to have others correct?

Thanks again for help.

EDIT:

This one was straight forward; =\

=> length FP / length FP-Shadow = Length FS / Length FS-Shadow

Please correct me if I am wrong; It could not be reconfigured as second because these are 2 sets of things, and it wouldnt make sense if I write as I wrote before.

In the second one we were talking about just men and days (one set of things,) not "Find the number of men and given the days spent working on one house and given the number of women and given the days spent working on one house.
If it was this case, the equation would be:


 number of men              number of women
---------------     =      -----------------
Days spent by men          Days spent by women




Please correct me if I am wrong. =\

Thanks.

This post has been edited by Nitewalkr: 03 April 2012 - 01:10 AM

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#11 Nitewalkr  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 03 April 2012 - 01:14 AM

Actually I think I am wrong entirely :(;

I'll look it up for questions related to the "divisive comparisons" and "Multiplicative comparisons." Thanks you for helping me understand this so far.
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#12 e_i_pi  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 03 April 2012 - 01:28 AM

You'd be better off looking up the terms "ratios" and "proportions".
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#13 SpartanGuy07  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 04 April 2012 - 07:10 AM

Quote

Please correct me if I am wrong; It could not be reconfigured as second because these are 2 sets of things, and it wouldnt make sense if I write as I wrote before.


I will correct you on this. Don't think of it as two sets of things. Think of it as *some* item (can be anything really) and it's shadow as a set. That's the same as men and the hours they work as a set. Therefore you can still set it up using a ratio.

For the flagpole question I would draw a picture. (You will see you have two similar right triangles.) From there it should be easier to see what measurements are needed in the ratio to calculate the correct answer.

Height of fence = 3
Shadow of fence = 4
Height of flagpole = x
Shadow of flagpole = 72

So I'd assume:

Height of fence        Height of flagpole
---------------   =    ------------------
Shadow of fence        Shadow of flagpole



should give you the correct answer.

Answer:
Spoiler

This post has been edited by SpartanGuy07: 04 April 2012 - 07:49 AM

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#14 peace_fixation  Icon User is offline

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Re: Differentiating between two Math questions.

Posted 04 April 2012 - 09:39 PM

Might I recommend this lecture series by Michael Starbird, I've been watching it out of curiosity lately and he explains the concept of similar triangles (which applies to the flagpole problem) really nicely, as well as other geometrical ideas.

Maths For The Visual World

For some intuition about this problem, maybe this will help.

Start by drawing the sun in the top corner of your page.

You have a flagpole of height X and it's shadow is 72 feet. Draw an upright line (the flagpole) and then draw a diagonal line from the top of the flagpole to the ground at the angle that the sun makes with the flagpole. Then draw the base (the shadow), it has a length of 72.

Now, you have a fence of height 3 feet, and its shadow is 4 feet. Draw a right angled triangle with a base of length 4, an upright side of length 3 and a diagonal at the angle that the sun makes with the fence.

The triangles are proportional (similar, the same shape but different scale) because they both depend on the angle of the sun to cast a shadow, so the angle of the diagonal (the hypotenuse) is the same for each triangle. Because of this, the ratio of the length of the straight sides is the same for each triangle, and this is why you can use the divisive comparison to solve for the unknown height of the flagpole.

My kingdom for Google Paint, I could have saved some time with a diagram I think!
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