83. This is an AI verification referring to my aunt. I didn't read the article and skimmed the comments.
How old is Ann?
71–76 of 76 posts
Re: How old is Ann?
#72Earlier quoted context omitted.
Sorry to say, the first half of this comment is almost gibberish. It became algebra when I introduced an unknown variable and wrote down an equation. I can't see a way to solve the problem without doing that. > If X is Ann's current age, then the problem setup is: 24 - x = x - 12 How did you get this equation from the problem statement? The equation is of course correct, but I don't see how you would derive it, other…
> Sorry to say, the first half of this comment is almost gibberish. In what way? > It became algebra when I introduced an unknown variable and wrote down an equation. But a lot of people, including me, can solve it without writing down any equation. > I can't see a way to solve the problem without doing that. Ah. So it's gibberish because of your limitations? That's... not how this usually works. (Although, to be fai…
I'll answer in reverse order.
I think what you suggest works! Putting it in the wording of my original comment: Mary IS 24, Ann WAS 12, and the same amount of time gets you from 12 to Ann's current age, and from Ann's current age to 24. I think it is obvious from there that you're half-way between, so Ann is 18. Thank you!
The part of your earlier comment I consider gibberish has nothing to do with the problem.
> It's slightly different, because you've supercharged your hammer.
This does not mean anything.
> Everything you ever understood about how to solve word problems has been subsumed into what your brain labels as "algebra."
This is bizarre speculation. Why are you analyzing my brain? I just asked for an explanation!
> Did you use algebra to convert the problem to algebraic form?
As you say, this is impossible to do, because it doesn't make sense. So why bring it up? It sounds like you are trying to convince me the problem is not algebra - or that I am in some way only seeing it as algebra because I am not thinking about the problem clearly. But I never said it was! I just said I can't see how to do it without algebra. Since you mixed those things up, I clarified by saying exactly what sense I was talking about algebra in the first place. Clearly that didn't work!
Again, thank you for explaining your reasoning, I appreciate it. Just leave out the analysis of my mind!
Re: How old is Ann?
#73Ann is 18. I think what makes it confusing is the "variable overloading" referring to both the current ages of Mary and Ann (M & A), and their ages at some point in the past "when Mary was as old as Ann is now" (M' & A'). So, what we're given is: M = 24 M' = A M = 2A' => A' = M/2 = 12 Since the age gap between Mary and Ann is constant, we know: M - A = M'- A' So, substituting in the known values: 24 - A = A - 12 2A =…
I think it’s easier to see if you drop the time indices and just introduce a variable for the elapsed time. So: Mary := 24 = 2(A - Δ) A = Mary - Δ And then it’s just substitution. But of course what appeals to one’s intuition is very personal
To me, explicitly representing the two pairs of ages (now: M, A; previously: M', A') is simpler because it let's you directly represent the problem statement without any mental gymnastics whatsoever.
M = 2A' "Mary is [now] twice as old as Ann was ..."
M'= A "when Mary was as old as Ann is now"Re: How old is Ann?
#74Earlier quoted context omitted.
> Sorry to say, the first half of this comment is almost gibberish. In what way? > It became algebra when I introduced an unknown variable and wrote down an equation. But a lot of people, including me, can solve it without writing down any equation. > I can't see a way to solve the problem without doing that. Ah. So it's gibberish because of your limitations? That's... not how this usually works. (Although, to be fai…
I'll answer in reverse order. I think what you suggest works! Putting it in the wording of my original comment: Mary IS 24, Ann WAS 12, and the same amount of time gets you from 12 to Ann's current age, and from Ann's current age to 24. I think it is obvious from there that you're half-way between, so Ann is 18. Thank you! The part of your earlier comment I consider gibberish has nothing to do with the problem. > It'…
You're welcome.
> Just leave out the analysis of my mind!
I should have added weasel words like "maybe" and "probably" because I don't know you. Yet, everything I wrote, I have observed numerous times in other people.
And (and of course, maybe I'm wrong here) if you hadn't learned algebra, this solution would have been more obvious to you. Obviously we can't run that experiment directly. But think back to your childhood. Did you ever intuitively know the answer to a problem that others struggled with? Does that happen as often lately?
Formal methods like algebra are powerful and allow us to document, step by step, transformations that would be impossible to hold in our heads informally. We can solve problems that were unapproachable before. But we can get so used to using them that we forget intuitive tricks that we used to use.
Maybe this didn't happen to you. You're right. I don't know you. I'm only extrapolating. It really is the sort of simple problem that many people (possibly most of them younger) can solve immediately without assigning variable names or even writing anything down.
If this describes your capabilities when you were younger, then something changed. What is it?
Let me give you an example of my own. When I was a child I would play around with electronics. I intuitively knew that if I put two resistors in parallel, the amount of resistance would go down, and by how much, and could easily extend that to 3 or 4 resistors, rummaging through my collection to find resistors that would parallel to give me the value I wanted.
Once I learned the parallel resistor formula, I got slower at everything above two resistors.
Which brings us to:
> As you say, [using algebra to convert the problem to algebraic form] is impossible to do, because it doesn't make sense. So why bring it up?
I brought it up because, although we agree that it is not strictly part of algebra, it is something that you had to learn in order to use algebra effectively.
To me (and of course, again, I'm still speculating here) the fact that you're smart enough to use intuitive methods to set the problem up in algebraic form means that you were probably smart enough to use intuitive methods to simply solve the problem directly, if you weren't so used to directing your brain activity towards doing things using algebra.
Re: How old is Ann?
#75Ann is 18. I think what makes it confusing is the "variable overloading" referring to both the current ages of Mary and Ann (M & A), and their ages at some point in the past "when Mary was as old as Ann is now" (M' & A'). So, what we're given is: M = 24 M' = A M = 2A' => A' = M/2 = 12 Since the age gap between Mary and Ann is constant, we know: M - A = M'- A' So, substituting in the known values: 24 - A = A - 12 2A =…
Thanks for sharing this, it actually makes it easy. I somehow convinced myself it was a trick having to do with ages being rounded off to whole numbers, so delta-age can be off by one... anyway I want my day back.
Re: How old is Ann?
#76Rephrasing it makes it easier to grasp: Mary is 24 years old. When Mary was Ann’s current age, Ann was 12 years old (half Mary’s current age). This makes it a bit easier to realize that Ann’s age has to be right in the middle of 12 and 24.
Personally, I would rephrase it to:
Ann is 6 years younger than Mary, who is 24 years old.
Or even better, Ann is 18 and Mary is 24.
But then again, I always disliked word-based logic problems that didn't correspond to genuine complexity. If something CAN be stated in simple terms, I believe it should be. If you want to create a word-based logic puzzle then present a genuine problem that can be engaged with rather than a poorly formulated explanation of the mundane.
That being said, I have no idea how I would present the same fundamental logical puzzle using a material problem that doesn't have a simpler distillation that solves the problem for you. Maybe I'm just not cut out for the realm of intellectual puzzles.