Comment by tempfile
8 hours ago
Mary IS 24. So Ann WAS 12. Say that was X years ago. Then Mary WAS 24-X and Ann IS 12+X. So 24-X=12+X, X=6, Ann is 18.
I can't see a way to do it without algebra.
8 hours ago
Mary IS 24. So Ann WAS 12. Say that was X years ago. Then Mary WAS 24-X and Ann IS 12+X. So 24-X=12+X, X=6, Ann is 18.
I can't see a way to do it without algebra.
there's 12 years between 12 and 24. it is divided equally between OldAnn-OldMary and OldMary-NowMary. 12/2=6, 12+6=18
It's a kind of cheating because it means not understanding the essence of the problem but with such small numbers enumeration is a viable strategy.
> Mary is 24 years old. She is twice as old as Ann was
So Ann was 12
> when Mary was as old as Ann is now
So Mary is older than Ann.
The age of Ann is somewhere between 12 and 24. Without much thinking I'd say that probably 12 and 24 are not included and probably it is an even number.
We can test each of them.
If Ann is 14 now, when Mary was 14 (10 years ago) Ann was 4 year old and Mary would be 8 now, this is not the solution.
If Ann is 16 now, when Mary was 16 (8 years ago) Ann was 8, Mary would be 16 now, nope.
If Ann is 18 now, when Mary was 18 (6 years ago) Ann was 12, Mary would be 24 now and she is. This is the solution.
Ann is 18.
It's not cheating, but it's not enlightening either.
> It's a kind of cheating because it means not understanding the essence of the problem
In my opinion, this method presumes a clear understanding of the problem itself.
If you didn't have a clear understanding of the problem, you would not be able to test an answer to see if it is correct.
Now, this clear understanding of the problem could, of course, be coupled with a lack of understanding of other methods available (such as algebra) to solve the problem.
OTOH, maybe it's just coupled with a clear understanding that with the working memory that you have available to you right at the moment and without writing anything down, you don't even need those other methods.
> I can't see a way to do it without algebra.
This is related to "When all you have is a hammer, everything looks like a nail."
It's slightly different, because you've supercharged your hammer. Everything you ever understood about how to solve word problems has been subsumed into what your brain labels as "algebra."
But look at it this way:
1) Did you use algebra to convert the problem to algebraic form? Probably not; algebra says nothing about word problems.
2) Once it was in algebraic form, did you need to repeatedly apply algebraic rules in order to reduce the problem, or could you glance at it and figure it out?
You may also be hampered by your choice of variable, because you chose "X" to be an intermediate variable.
If, instead, you choose "X" to be what you are searching for, Ann's current age, then the problem setup is:
Which many of us can solve in our heads without writing down, or even without consciously converting "Ann's current age" to "X".
Uhhh... what? The OP is right; even if you do it intuitively it's still algebra. If you need a proverb to justify it: Just because your hammer is made of stone doesn't make it less of a hammer.
Thanks for the downvote.
Look, when someone says "you need algebra to solve this" is it reasonable to assume that they are talking about informal methods that people have used forever, or is it more reasonable to assume they are talking about formal algebraic methods?
Because many people sure as shit don't need any algebraic symbols or operators to solve this in their heads.
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 than writing down a more obvious equation and rearranging it.
> 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 fair, it's often the case that people of limited intellectual means lash out with unkind comments such as "gibberish" so maybe this is how it works.)
> How did you get this equation from the problem statement?
"Mary is 24 years old. She is twice as old as Ann was when Mary was as old as Ann is now. How old is Ann?"
We know that there is a delta between Mary's current age (24) and what I called X in my previous comment (Ann's current age AKA Mary's prior age). That would be 24 - X.
We also know that at some previous time, Ann was 12 (half of 24) when Mary was (Ann's current age AKA Mary's prior age).
Some of us just take the mental shortcut that the in between age has to be the average of 24 and 12 (because the delta doesn't change[1], so the delta must have been the same before as it is now), but if forced to write it down into algebra, we can say that this second statement is X - 12.
And then of course, again, because the delta doesn't change, and the delta is equal to both x-12 and 24-x, those expressions must be equal to each other.
[1] Except of course, the delta could wobble a bit for birthdays being on different dates within the year. In simple puzzles like this, of course, that +/- 1 year possibility is usually ignored.