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Algebra word problems

 
 
Reply Tue 29 Dec, 2009 02:42 pm
Ellen is 11 years older than Maja.
Last year Ellen was twice as old as Maja.
How old is Maja now?
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engineer
 
  1  
Reply Tue 29 Dec, 2009 02:52 pm
@summer morning,
Set up your variables. Let X by Maja's age and Y by Ellen's age.

Ellen is 11 years older than Maja => Y = X + 11
Last year, Ellen's age was Y-1 and Maja's age was X-1.
Last year, Ellen was twice as old as Maja => Y-1 = 2 (X - 1) so Y=2X-1
X+11 = 2X-1
X=12
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MorganBieber
 
  0  
Reply Sat 2 Apr, 2011 09:33 am
@summer morning,
Maja is now 7 years old.
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raprap
 
  1  
Reply Fri 22 Jul, 2011 09:48 am
Let M be Maja's are and E be Ellen' age

E=M+11
E-1=2(M-1)

then E-M=11 & E-1=2M-2 or 2M-E=1

Add the two together

M=12 & E=23

The secret to word problems is to simplify and write down what you know and then check your answer

23=12+11
23-1=2(12-1)

Rap
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AndyCharles
 
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Reply Wed 3 Aug, 2011 07:30 am
@summer morning,
Hi Friend,

Thank you for sharing your information. Really I am very appreciated here and this is the very useful information.
The first strategy is to understand the language content of the problem.
The second is recognizing that a science word problem is an application of algebra. Third, the values described in the problem are interconnected.
Fourth, determine the appropriate algebraic equation for the problem. Finally, document the entire problem solving process. Successfully completing science word problems require well reading comprehension skills. Word problem solvers cannot effectively complete the word problem without understanding the problem itself. Word problems in science are applications of algebraic expressions, or equations. Good word problem solvers distinguish between the given in the problem and the value, which is to be calculated. Successful science word problem solvers see how the mathematical expressions in the statements are interconnected to each other. Successful problem solvers determine the appropriate algebraic expression, or equation, for the problem. Successful problem solvers document their thinking process by writing out each step that he uses to solve the problem.

Thanks
Andy Charles
_________________
Edit [Moderator]: Link removed
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raprap
 
  1  
Reply Thu 4 Aug, 2011 01:03 pm
Quote:
G. Polya, How to Solve It
Summary taken from G. Polya, "How to Solve It", 2nd ed., Princeton University Press, 1957, ISBN 0-691-08097-6.
UNDERSTANDING THE PROBLEM
First. You have to understand the problem.
What is the unknown? What are the data? What is the condition?
Is it possible to satisfy the condition? Is the condition sufficient to determine the unknown? Or is it insufficient? Or redundant? Or contradictory?
Draw a figure. Introduce suitable notation.
Separate the various parts of the condition. Can you write them down?
DEVISING A PLAN
Second. Find the connection between the data and the unknown. You may be obliged to consider auxiliary problems if an immediate connection cannot be found. You should obtain eventually a plan of the solution.
Have you seen it before? Or have you seen the same problem in a slightly different form?
Do you know a related problem? Do you know a theorem that could be useful?
Look at the unknown! And try to think of a familiar problem having the same or a similar unknown.
Here is a problem related to yours and solved before. Could you use it? Could you use its result? Could you use its method? Should you introduce some auxiliary element in order to make its use possible?
Could you restate the problem? Could you restate it still differently? Go back to definitions.
If you cannot solve the proposed problem try to solve first some related problem. Could you imagine a more accessible related problem? A more general problem? A more special problem? An analogous problem? Could you solve a part of the problem? Keep only a part of the condition, drop the other part; how far is the unknown then determined, how can it vary? Could you derive something useful from the data? Could you think of other data appropriate to determine the unknown? Could you change the unknown or data, or both if necessary, so that the new unknown and the new data are nearer to each other?
Did you use all the data? Did you use the whole condition? Have you taken into account all essential notions involved in the problem?
CARRYING OUT THE PLAN
Third. Carry out your plan.
Carrying out your plan of the solution, check each step. Can you see clearly that the step is correct? Can you prove that it is correct?
Looking Back
Fourth. Examine the solution obtained.
Can you check the result? Can you check the argument?
Can you derive the solution differently? Can you see it at a glance?
Can you use the result, or the method, for some other problem?


http://www.math.utah.edu/~pa/math/polya.html

Rap
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