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## Main Question or Discussion Point

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?

- Thread starter 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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- #3

Mark44

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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 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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Office_Shredder

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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

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- #7

Mark44

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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?

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Office_Shredder

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OK if I had rewritten the equations as

2y = x

2x = y

would you have picked the 2x=y choice then?

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Mark44

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The fact that x appears before y should not steer you toward writing x = ...

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Mark44

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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)

If you write y = 2x, the units are saying apples = apples/person * person, so the left and right sides represent the same unit - apples.

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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 [itex]x[/itex] people and [itex]y[/itex] apples. Each person holds two apples.

2. There are [itex]y[/itex] apples and [itex]x[/itex] 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 [itex]y[/itex] and continue from there.

[itex]y[/itex] is twice the number of apples.

[itex]y[/itex] is twice [itex]x[/itex].

[itex]y[/itex] is [itex]2x[/itex].

[itex]y[/itex] = [itex]2x[/itex].

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I just wanted to thank you folks for your help, it's actually making more sense now :).

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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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