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7 is a distance of 18 from n, then what does n equal?

Thank you very much.

And what's difference if I replace "a" with "the"? 7 is the distance of 18 from n.

It is a little trick, really. I can't get a grip of it.

Davkett · Accepted Answer

Is this a riddle, Jeff? Is there any other context?

P.S.: (The phrase is , 'I can't get a grip on it.')

Jeff_999 · Answer

Thank you, Davkett. <img class='emoticon' style='Width:19px;Height:19px;' data-delaysrc='https://uat-englishforward-forums-backend.s3.us-west-2.amazonaws.com/Emoticons/1.gif' src='https://uat-englishforward-forums-backend.s3.us-west-2.amazonaws.com/Emoticons/1.gif' alt='Emotion: smile'/> That's a whole mathematic thing.

Davkett · Answer

n = -11

?

Jeff_999 · Answer

Yes, that's the one. The equation is:

|7-n| = 18

Then we get:

n = -11 and 25.

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But the problem is I misunderstood the sentence "7 is a distance of 18 from n". I thought the number 7 was the distance. Then |n-18| = 7. Since I am not a native speaker, some expressions in English confront with my Chinese-background logical thinking, if you know what I said. So, could you please explain it for me?

And if the question is rephrased as "7 is the distance of 18 from n", what the result will it be?

Thank you.

Davkett · Answer

I was afraid of something trickier here, Jeff, because I had two answers for n: -11 and 25. I thought if only one answer was correct, it would be : ~~11. I can hardly explain what my logic was, though~~-it had something to do with musing over the word, 'from'.

[n-18] = 7..... gives the same two answers, I think. (But I'm not a mathematician.)

Replacing 'a' with 'the' doesn't change anything critical for me. 'The' is a bit more emphatic (and maybe more correct, since every other number that is a distance of 18 from n changes the value of n. The only number that is a distance of 18 from n is 7 if the answer to n is -11 and 25.)

CalifJim · Answer

"distance of 18" is used in the same way as we would use any unit of measure.
How far is the stadium from the church?
The stadium is a [mile / kilometer / distance of seven miles] from the church.
The stadium is *the [mile / kilometer / distance of seven miles] from the church.

It's not a particular, specific mile, kilometer, or distance, so it can't be the distance.

Analogously, How far is 7 from n? 7 is a distance of 18 from n.

Alternately, however, and this may be the source of your confusion,
The (specific, measured) distance between the stadium and the church is [a / *the] [mile / kilometer / distance of seven miles].
Hence,
The (specific, measured) distance between 7 and n is [a / *the] distance of 18 (unspecified units).
CJ

Jeff_999 · Answer

Thank you, Davkett.

So, can I rewrite the question
"On a certain number line, if 7 is a distance of 18 from n then n = ?"
as
"On a certain number line, if 7 from n is a numeric value 18 then n = ?"

I guess I was caught up with a distance of 18.

Jeff_999 · Answer

Ohh Thank you CJ. I just saw your explanation, after submitting my post.

So, "7 is a distance of 18 from n" is asking us "how far is 7 from n"?

I was stuck in understanding "a distance of 18". Now it's clear.

And I was kinda misled by my classmate who said we would get different answer if we were asked "7 is the distance of 18 from n". Hehe. never thought it was wrong. We all got wrong "distance of 18".

Thank you again.

Jeff_999 · Answer

This morning, I checked the thread again. I guess I didn’t understand you quite well last night, ‘cause I was a little hasty to reply your post.

Now it appears clearer when I carefully go thru your explanation again.

"distance of 18" is used in the same way as we would use any unit of measure.
How far is the stadium from the church?
The stadium is a [mile / kilometer / distance of seven miles] from the church.

So, on a certain number line, 7 has its corresponding point (just like we put stadium on that point), so does n. The question is we don’t know where’s the point n for the moment. But we know that the distance from 7 to n is 18 (which refers to the length of a straight line, not a point as 7 or n).

Did I get it right?

I suppose what other students and I got wrong is:
we mistakenly took "7 is a distance of 18 from n" as "(let's say 7 miles) 7 miles is the distance between/from 18 and n". Then we got the equation:
7 = |18-n|.
Actually if we want to express the distance or the length between two positions, we have to add a unit of length after a certain number (like 7 miles. We can't leave out miles, right?), or say "a distance of + a certain number" (we don't need a unit of length, right?). So "7 is the distance" makes no sense. It has to be "7 miles or kilometers is the distance."

It doesn't matter what I just said last night.

I am trying to make your teachers proud. Please reply it to lemme know I got it all right.

CalifJim · Answer

So, on a certain number line, 7 has its corresponding point (just like we put stadium on that point), so does n. The question is we don’t know where’s the point n for the moment. But we know that the distance from 7 to n is 18 (which refers to the length of a straight line, not a point as 7 or n).

Did I get it right?

Yup!

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