Precalc Woes...

[TC10284]

Hey all

I need some assistance with precalc. First of all, I am not asking you to solve it for me. These are word problems and I'm having the worst time trying to figure out how to just set them up to begin. If I can figure out how to set it up, I can almost bet I can get the rest of course. I have a few but for now I'll just do one.

This one involves a person wanting to fence off a square feeding lot and then the yplan to cross-fence the lot to divide it into four smaller square feed lots. If the person uses 480 feet of fencing, how much area will be fenced in?

I have tried
2L + 2W = 480
L + W = 240 (divded above by 2)
and then tried to split that into (120 + X)(120 - X) but I am not getting the correct results according to the book.
Sigh...=/

 

[BrownTown]

6400?

 

[CycloWizard]

I think it should be 3L+3W=480. This is because you have three fence segments running in the x direction (top, bottom, and the divider) and three in the y direction (left, right, and divider). The area covered is then L*W.

Edit: since it's a square, L=W such that 6W = 480 and W = 80 ft. Thus, A = L*W = W^2 = 6400 ft^2.

 

[BurnItDwn]

Draw a picture of it.

Notice that there are 3 horizontal rows, and 3 vertical rows.

if it's a "square" then L = W

should be really simple from here

assuming it is square, you should reach the same conclusion that BrownTown did

 

[BrownTown]

yeah, thats pretty much what i did. Drawing pictures of problems is a good way to get going if it isn't immidiately obvious

 

[TC10284]

OK, so I guess 6W is coming from the 3 rows and 3 columns of the fence. And when you say W = 80, that's from dividing 480 by 6 (W = 80). I'm confused from this part on how to solve it.

God....WTF....What is missing from my DNA or what is physically wrong with my brain to NOT see things in word(application) problems...dang it!!

 

[nsadhal]

Well, you're on the right track now. You know that L=W and W=80... you want to find the area that's fenced in correct?
A = L*W. The picture should help here if you're still not getting it.

 

[CycloWizard]

Originally posted by: TC10284
OK, so I guess 6W is coming from the 3 rows and 3 columns of the fence. And when you say W = 80, that's from dividing 480 by 6 (W = 80). I'm confused from this part on how to solve it.

God....WTF....What is missing from my DNA or what is physically wrong with my brain to NOT see things in word(application) problems...dang it!!

Here is how to solve a word problem:

1. Write down everything given for the problem in a list. For example, total fence length = 480 ft.
2. Write down what you're trying to find. For example, area = ?.
3. Write down the formulas that apply to what you're trying to find. For this problem, first you would write down area = length * width.
4. Consider what terms in #3 you don't know. For this problem, you know it's a square, so length = width. Simplify #3 accordingly: area = length * length.
5. Repeat #4 until you have an equal number of equations and unknowns, then solve. You may have to generate some of the equations, which is the tricky part that just takes practice. In this case, the only equation you have to come up with on your own is the 3W+3L = 480, then the rest is done for you using the above procedure.

I really think the key to solving this type of problem is using the same procedure over and over, rather than trying to wing it for each one.

 

[Vegitto]

This'd be much easier if I'd understand the question. Apparently, English not so good.

 

[BrownTown]

in response to CycloWizard, i'd say its not always a good idea to use the same method for all problems. Alot of teachers i've had have try to tech this type of philosophy, but alot of times it much easier to at least consider using a customized aproach and then falling back on the more methodical way if that does not work. Your way will likely yield the right answers very often, but in alot of cases you end up wasting time doing it this way. For example, this problem does not require a long drawn out process to solve. IF you just think about this problem in your head it takes maybe 15 secodns to solve, but if you do all the stepts you suggested its probably gonna take a couple of minutes. I think the way you described works best in multivariable situations where a single function cannot be easily obtained.

I mean i could certainly use the following equations:

l = length of a side
A = area

6l = 480
A=L^2

But both equations are trivial to solve and you can immidiately go right to the answer without the interveaning steps.

You method does work increadibly well for node and loop analysis of electric circuits, or for alot of the type of problems you see in calculus.

 

[TC10284]

My problem is that even with a picture it's hard to envision or imagine these things. It is so disheartening to me because I can do a lot of things computer/network related but not a few sentences on a piece of paper.

 

[BrownTown]

well, just draw the picure of the problem, you have a square with 4 sides, and then you have 2 cross pieces in the middle to divide the square into 4 smaller squares, it should be pretty clear that all 6 pieces are of the same length, therefore you need 480/6 means that each piece is 80ft long. Then since this is a square the total area is length^2, so 80^2 = 6400

AAAAAAAAAAAAAAAAAAAA
A---------------A---------------A
A---------------A---------------A
A---------------A---------------A
A---------------A---------------A
A---------------A---------------A
AAAAAAAAAAAAAAAAAAAA
A---------------A---------------A
A---------------A---------------A
A---------------A---------------A
A---------------A---------------A
A---------------A---------------A
AAAAAAAAAAAAAAAAAAAA

well, thats sorta waht it loks like, hopefully you can see the 3 vertical pieces, and hte 3 horizontal pieces and see where the equation comes from

d@mn forum keeps screwing up my pictures, hope this works

 

[TC10284]

Hehe...yes, I can get the picture, but most of the times that helps a little but not to solve it completely.

 

[inveterate]

U must be white, LOL

 

[inveterate]

U must be white, LOL

 

[TC10284]

What do you mean by that?

 

[Loki726]

13333333333333333336
1---------------5---------------6
1---------------5---------------6
1---------------5---------------6
1---------------5---------------6
1---------------5---------------6
14444444445444444446
1---------------5---------------6
1---------------5---------------6
1---------------5---------------6
1---------------5---------------6
1---------------5---------------6
12222222222222222222

See how there are 6 sides all with equal length. So divide the total length by six to get the length per side. Now the length (Side 1) is 80ft, and so is the width (Side 2). The area is just 80^2 = 6400 ft^2.

 

[CycloWizard]

Originally posted by: BrownTown
in response to CycloWizard, i'd say its not always a good idea to use the same method for all problems. Alot of teachers i've had have try to tech this type of philosophy, but alot of times it much easier to at least consider using a customized aproach and then falling back on the more methodical way if that does not work. Your way will likely yield the right answers very often, but in alot of cases you end up wasting time doing it this way. For example, this problem does not require a long drawn out process to solve. IF you just think about this problem in your head it takes maybe 15 secodns to solve, but if you do all the stepts you suggested its probably gonna take a couple of minutes. I think the way you described works best in multivariable situations where a single function cannot be easily obtained.

I mean i could certainly use the following equations:

l = length of a side
A = area

6l = 480
A=L^2

But both equations are trivial to solve and you can immidiately go right to the answer without the interveaning steps.

You method does work increadibly well for node and loop analysis of electric circuits, or for alot of the type of problems you see in calculus.

Of course you're right. I'm just trying to offer a tried-and-true method to learn how to solve these problems that works pretty much every time. Once he's got the hang of it, I'm sure he'll figure out how to neglect the tedious steps and cut to the chase.

 

[DrPizza]

For what it's worth, "OK, so I guess 6W is coming from the 3 rows and 3 columns of the fence. And when you say W = 80, that's from dividing 480 by 6 (W = 80). I'm confused from this part on how to solve it." If you're confused from this part, then I disagree with this "If I can figure out how to set it up, I can almost bet I can get the rest of course." You are probably going to need help throughout the course. There are usually people here willing to offer assistance, but if the volume gets overwhelming, and for the sake of time, you may want to find a friend who can help you in person.

 

[LumbergTech]

if you want a good spot to get help..on IRC go to the efnet network and join the #math channel..there are some really helpful individuals there..make sure you read the channel rules first so you know how to pose questions without upsetting people

 

[mjia]

Originally posted by: CycloWizard
Here is how to solve a word problem:

1. Write down everything given for the problem in a list. For example, total fence length = 480 ft.
2. Write down what you're trying to find. For example, area = ?.
3. Write down the formulas that apply to what you're trying to find. For this problem, first you would write down area = length * width.
4. Consider what terms in #3 you don't know. For this problem, you know it's a square, so length = width. Simplify #3 accordingly: area = length * length.
5. Repeat #4 until you have an equal number of equations and unknowns, then solve. You may have to generate some of the equations, which is the tricky part that just takes practice. In this case, the only equation you have to come up with on your own is the 3W+3L = 480, then the rest is done for you using the above procedure.

I really think the key to solving this type of problem is using the same procedure over and over, rather than trying to wing it for each one.

I don't really support using strategies for solving problems by searching for formulae that satisfy the required values. You will effectively end up simply be looking for equations that provide the approriate units. This might work for earlier level courses, but it certain doesn't for anything more advanced ones. Try to focus on concepts.

Back when I was taking physics, many students used the technique of memorizing equations and picking the one that had the units used in the provided values and answer. That worked for 80% of the questions, and they usually did alright, but they didn't really understand what they were doing or what the equations they were using meant or how/why they were derived.

 

[BrownTown]

What CycloWizard is describing is actually a very good method for solving complex problems in a simple and methodical manor. Hes not suggestingn you just find an equation and plug numbers in. The point is to find relationships in the known quantities and then to write the relationships as equations. If the question is solvable there should be at least as many unique equations as there are unkowns. Then you cna use methods like substitution or matricies to solve for all the unkowns. This is exactly what they teach for solving circuit problems in electrical engineering. And it works jsut as well for any other problem where you have many unknowns all of which are related via certian equations.

The method of solving problems by just manipulating values to get the right units is a sneaky way of solving problems if you don't know what you're actually supposed to do. I'd only suggest it as a last resort, but even my AP physics teacher taught us to do it if you can't think of anything better. I'd also sugggest that when you do solve a problem you should always make sure that het units really do cancel correctly, its an easy way to check whether or not an answer is right. I know personally ive had times where i forgot whether or not i was supposed to square a term or not, and cancelling the units yielded the answer.

 

[TC10284]

DrPizza,
No disrespect but that did frighten me a little. I have never been good with word problems and I have a 3.8+ GPA at my community college (yes, I realize this is just a community college) that concerns me if I do poorly in the class.

I am trying, it's just math has never been my subject (probably one reason I dislike programming and favor hardware/networking). Luckily, I do have some help, my GF is very skilled at word problems and other math (probably why she likes programming lol). It's just she's not here all the time.

I can pull out most of the information now, it is just that I cannot easily start a formula. My GF says that I'm trying to make things too complicated or that I'm trying to do to much work at once. But, I was not able to do any of the problems without her help unfortunately =/
Friday was the last day spent on that section, but, I'd still like to be able to do them. :disgust:

 

[BrownTown]

what exactly is your major?, and how far in math are you expected to go in that major?

 

[TC10284]

My current major is Networking Tech. I've already got my two year IST degree and only have one more semester for my two year Net. tech degree.

At my community college I've met all the math requirements (MAT 140 is all for Networking or IST) but for a university, most that I've seen want at least MAT 171 (precalc which is what I'm taking now) or more (at least I think, but I am not certain of this) if I decide to go for anything higher than a BS.