Word Problem Confusion: Am I Right or Nitpicky?

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Discussion Overview

The discussion revolves around the interpretation of word problems involving relationships between quantities, specifically focusing on the correct formulation of equations based on given variables. Participants explore whether the order of variables in a problem statement affects the correctness of the equations derived from them.

Discussion Character

  • Debate/contested
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • Some participants express confusion about whether the program's insistence on a specific equation format is nitpicky or if it reflects a misunderstanding of the problem.
  • Others argue that the two equations y=nx and x=ny represent different relationships unless n equals 1, suggesting that only one can be correct in a given context.
  • A participant mentions encountering problems where the order of variables seems to dictate the formulation of equations, questioning if there is a specific phrase to guide understanding.
  • One participant provides a specific example involving people and apples, leading to a discussion about the correct interpretation of the relationships and the resulting equations.
  • Another participant emphasizes the importance of units in equations, arguing that only one formulation makes sense in terms of units, and that the order of variables should not dictate the equation's structure.
  • Some participants express uncertainty about their understanding of the problem and the equations, indicating a struggle with abstract symbols and their implications.
  • A later reply challenges a previous explanation, asserting that the final interpretation of the relationships must remain consistent with the definitions of the variables involved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the equations derived from the word problems. There are competing views regarding the significance of variable order and the correctness of the equations based on the context provided.

Contextual Notes

Participants highlight limitations in their understanding, including potential misinterpretations of the problem statements and the implications of variable order on the equations. There is also mention of unresolved mathematical steps in deriving the correct relationships.

Tyrion101
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I will occasionally get problems wrong because the "right" answer should be y=nx, but I put x=ny, is the program being nitpicky or am I somehow misreading the problem?
 
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Since those are two different equations (unless n happens to equal 1), there is nothing nitpicky about accepting only one of them as correct. It sounds like you may be misreading the problem, but without showing us a specific example it is difficult to say with certainty.
 
Tyrion101 said:
I will occasionally get problems wrong because the "right" answer should be y=nx, but I put x=ny, is the program being nitpicky or am I somehow misreading the problem?
The program is not being nitpicky. You might be misreading the problem or there might be something else going on. Without more information, it's hard to say.
 
I've run into problems where y comes before x, but have to resort to just going with what is stated as the right answer for those kinds of problems without really understanding why I put y first. Is there a phrase I can look for or something?
 
Can you give a specific example? There's no phrase you should look for, you should just properly understand the problem.

Is this an example where you would get it wrong? There are x people, and each of them are holding 2 apples. Let y be the number of apples. Which of the following is true?
y=2x
x=2y
 
To my mind, if there are x people and y apples, x would come first because that is what was stated first so in my mind x= 2y
 
Tyrion101 said:
To my mind, if there are x people and y apples, x would come first because that is what was stated first so in my mind x= 2y
I think you might be getting lost with abstract symbols.

If there are 8 people (x = 8) and each of them has 2 apples, then how many apples are there in all?
 
Solving it as 8=2y I get 4, shouldn't it be 16? Or am I again getting lost? I think I may see where you're going
 
Tyrion101 said:
To my mind, if there are x people and y apples, x would come first because that is what was stated first so in my mind x= 2y

OK if I had rewritten the equations as
2y = x
2x = y

would you have picked the 2x=y choice then?
 
  • #10
Tyrion101 said:
To my mind, if there are x people and y apples, x would come first because that is what was stated first so in my mind x= 2y
The fact that x appears before y should not steer you toward writing x = ...
 
  • #11
Tyrion101 said:
Solving it as 8=2y I get 4, shouldn't it be 16? Or am I again getting lost? I think I may see where you're going
Yes, it should be 16. If there are 8 people, and each has 2 apples, then the total number of apples couldn't possibly be 4, could it?

Furthermore, only one formulation makes sense in terms of the units. Each variable (or number) also has units.


x (persons)
2 (apples/person)
y (apples)

If you write x = 2y, the units are saying persons = apples/person * apples. The left and right sides don't agree - the right side would be (apples)2/person, which is nonsensical.

If you write y = 2x, the units are saying apples = apples/person * person, so the left and right sides represent the same unit - apples.
 
  • #12
Tyrion101 said:
Solving it as 8=2y I get 4, shouldn't it be 16? Or am I again getting lost? I think I may see where you're going

Exactly. The correct answer is 16. Of the two equations Office_Shredder offered to you, the one you chose yielded an incorrect answer. Therefore, the equation you chose is not an accurate model of the situation described. Whenever possible, you should test your equation as an accurate model.

You are placing too much importance on the order in which variables appear in the phrasing of the problem. Consider the following two (equivalent) phrasings:

1. There are x people and y apples. Each person holds two apples.

2. There are y apples and x people. Each person holds two apples.

Each phrasing corresponds to an equation. The meaning of the phrasings are identical. Therefore, the corresponding equations should be identical.

In modeling the situation described in a world problem with a mathematical equation, you may find it helpful to gradually transition from the English language to the language of mathematics. For example, we could express the relationship between the number of people and the number of apples as the following English sentence:

The number of people is twice the number of apples.

Now, begin replacing the English components with appropriate mathematical symbols. We will start by replacing the phrase "the number of people" with the variable y and continue from there.

y is twice the number of apples.

y is twice x.

y is 2x.

y = 2x.
 
  • #13
I just wanted to thank you folks for your help, it's actually making more sense now :).
 
  • #14
If hope the sense your making is not based on QED Andrews post because it is incorrect.

His example starts with x as number of people and y as number of apples, then at the end switches to y as the number of people and states that y (the number of people) is twice x (the number of apples)... which would be incorrect.

What he meant to say is that if y is the number of apples, then y is twice x (the number of people) because each person has two apples.

Or that if y is the number of apples, then x (the number of people) is one half of y because each person has two apples.
 

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