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Question 1210606: four more than three times n equals -5
Found 5 solutions by josgarithmetic, greenestamps, KMST, ikleyn, Edwin McCravy:
Answer by josgarithmetic(39832)   (Show Source):
You can put this solution on YOUR website! Literally  , word for word, symbol for symbol
Nothing there to be taught. The worded description presents no ambiguities and is extremely simple, so the symbolism can be taken word for word.
Answer by greenestamps(13362)  (Show Source):
You can put this solution on YOUR website!
Here, copied exactly, is the response from the other tutor:
Literally , word for word, symbol for symbol
That is NOT a good way to teach students how to learn to do algebra.
I have seen many students struggle with learning algebra because they do what that tutor says -- translating the words into a mathematical statement word for word.
That is NOT the right thing to do.
It is important to understand what the whole written phrase means; you should not do the translation word for word.
The phrase "four more then three times n" means you started with 3 times n and added 4 more. So the correct translation is "3n+4" instead of "4+3n".
It is true that, algebraically, those two phrases are equivalent. So setting up the problem using either one will not cause a problem.
But what if the phrase were this: "four less than three times n"
A word-for-word translation of that would give you "4-3n".
But that is not what the whole phrase says. The phrase says you started with the 3n and then subtracted 4. So the correct translation is "3n-4".
And the two mathematical phrases "4-3n" and "3n-4" are not equivalent.
So DO NOT translate written statements word for word into mathematical statements. It is necessary to understand the real meaning of the written words in order to write the correct mathematical statements.
Answer by KMST(5385)  (Show Source):
You can put this solution on YOUR website! As a written statement, that statement, without any commas, could lead itself to puzzlement, or misinterpretation.
If someone makes that statement orally, I would pay attention to the pauses for clues about its meaning.
If I detect a pause after "more" or after "than", I have heard "four more", or "four more than",
I expect that I have to add the number 4 to whatever comes afterwards.
Then, the phrase "three times n" that comes afterwards seems to be an independent quantity, so I expect that I have to multiply the number 3 times the value of n, that is unknown for now.
In that case, I could write the equation as 4+(3n)=-5, or (3n)+4=-5.
However, due to a long ago established and universally agreed upon custom, I know I do not need to write those brackets.
So, I would write or  to start.
Then, I would add  to each side of the equal sign (same as subtract 4 each side of the equal sign) to get
 or  .
Then I simplify those expressions to get  .
The next step would be to multiply each side of the equal side by  (same as dividing each side by 3) to get
 , which simplifies to  .
My Spidey-sense tells me this is what the teacher meant,
and that the teacher would be happy with a short response like
-->  --> --> 
On the other hand, if the first pause I detect is after "three", I have heard the phrase "four more than three", which to me means to calculate the sum 3+4=7.
Then, if "times n" comes afterwards, I expect to multiply 7 times n.
In that case I would write  --> -->
Answer by ikleyn(53906)  (Show Source):
You can put this solution on YOUR website! .
Regarding this incoming problem, tutor @KMST made a remarkable discovery: she found that in this task
(which appears simple at first glance) there exists an alternative, unexpected reading/interpretation
which completely changes the game. I am impressed by the @KMST' discovery.
I looked at some other web-sites, and they all as one treat the problem as "4 + 3n = -5".
@KMST showed that, alongside the traditional interpretation "4 + 3n = -5,"
a completely different interpretation is possible: "(4 + 3)n = -5",
and, moreover, both versions are equally valid.
This demonstrates that even in cases that seem straightforward at first glance, hidden pitfalls may exist.
Thus, only in simple cases verbal quantitative descriptions are secure.
In more complicated cases, verbal descriptions simply do not work and leave room for various interpretations.
This is why in Mathematics (and in Science, in general), starting from a certain level of complexity,
that kind verbal descriptions are considered as dangerous and NEVER used in serious texts.
They have been displaced by precise mathematical expressions 200 or 300 years ago, when the modern/contemporary
Math language was created.
I think that the time, when such wording exercises were actual from the educational point of view,
gone forever approximately 200 years ago, and the attempts to construct any sort of educational framework
upon this foundation are simply laughable - same as attempts to turn back the hands of time.
Regarding this remarkable post by @KMST, I only want to warn a reader about her typo:
in cases when she interprets "-4 - 5" as "-7", a reader should read "-4 - 5" as "-9".
Answer by Edwin McCravy(20086)  (Show Source):
You can put this solution on YOUR website!
Stated problems in algebra are problematic because English does not have
'order of operation' rules like algebra, so sometimes they are ambiguous.
Four more than three times n equals -5
If that were meant to be interpreted this way:
(Four more than three) times n equals -5
it would be (3+4)n = -5
7n = -5
n = -5/7
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However, if it were meant to be interpreted this way:
four more than (three times n) equals -5
it would be 3n+4 = -5
3n = -9
n = -3
I would assume that it is to be interpreted this way, using the operations of
mathematics (multiplication before addition). Also, if you are taking algebra,
no intelligent teacher would likely be testing you to see if you could do
something as elementary as adding 3+4 to get 7.
Edwin
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