How old are Nathan and Axel?
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The sum of the current ages of Nathan and Axel is 49. Nathan is twice as old as Axel was when Nathan was as old as Axel is now.
How old are Nathan and Axel now?
Please put answers and solutions in spoiler tags. You must show your work for the beer.
Quote: WizardI've been waiting for an answer to my cannonball problem since April 20. Maybe I need to go back to something a bit easier. That said, here is your next math problem. Winners of a beer within the last year are on a 24 hour hold.
The sum of the current ages of Nathan and Axel is 49. Nathan is twice as old as Axel was when Nathan was as old as Axel is now.
How old are Nathan and Axel now?
Please put answers and solutions in spoiler tags. You must show your work for the beer.
Answer must be divisible by 7 for the ratios to work. When Nathan was 21 (Axel's age now), Axel was 14 (half Nathan's age now ).
28+21 = 49.
(4*7)-7=(3*7)
(3*7)-7=(4*7)/2
[1] N+A=49
[2] N=2(A-(N-A))
From [2]:
N=2(2A-N)
=4A-2N
3N=4A
N=(4/3)A
From [1]:
N+A=49
(4/3)A+A=49
(7/3)A=49
A=49*(3/7)=21
N=(4/3)A=(4/3)*21=28
Same result via more tedious calculations.
Quote: WizardCongratulations to both Doc and Barb for the right answer. For the beer I require more than a proof that the answer is right, but a process for finding the answer, which Doc satisfied. So, congratulations Doc. I owe you a beer and you're now on the 24-hour hold list until 5/6/2020.
Pbbbbbb...
Quote: WizardCongratulations to both Doc and Barb for the right answer. For the beer I require more than a proof that the answer is right, but a process for finding the answer, which Doc satisfied. So, congratulations Doc. I owe you a beer and you're now on the 24-hour hold list until 5/6/2020.
Since doc has never drank in his life I will gladly accept on his behalf
Maybe I can come up with a better idea, but GWAE is correct regarding the low likelihood of my collecting this prize myself.
But thank you, Wizard. I appreciate the recognition of old-school algebra techniques, though I didn't really stick to all of the old rules.
Quote: WizardCongratulations to both Doc and Barb for the right answer. For the beer I require more than a proof that the answer is right, but a process for finding the answer, which Doc satisfied. So, congratulations Doc. I owe you a beer and you're now on the 24-hour hold list until 5/6/2020.
I think that is crap.
In 9th grade Algebra we had a test of 10 story problems like this. I was the only one in the class to get 10 out of 10 and the teacher failed me. "You didn't show your work". Sorry, I am smart enough to do these in my head. I am still bitter about it.
That teacher is dead and I am not upset about it.
Quote: DRichI think that is crap.
In 9th grade Algebra we had a test of 10 story problems like this. I was the only one in the class to get 10 out of 10 and the teacher failed me. "You didn't show your work". Sorry, I am smart enough to do these in my head. I am still bitter about it.
That teacher is dead and I am not upset about it.
That was pretty much high school algebra for me too, constantly had grades docked for having correct answer but not showing work. Course/questions dumbed down to the lowest denominator so badly that I never saw any point to actually learning algebra until years later when all they give you are problems so simple it’s easy to figure out without having to write it down.
Quote: DocAnd here I was, pondering whether there was a polite way to pass the reward along to BBB without being offensive to the Wizard. Maybe I should offer it up as a challenge, such as my beer credit goes to the first person to show up at Spring Fling wearing a mask that out-performs the one worn by darkoz. (Disqualifying any member of the darkoz clan, who likely would really be wearing a darkoz original.)
Maybe I can come up with a better idea, but GWAE is correct regarding the low likelihood of my collecting this prize myself.
But thank you, Wizard. I appreciate the recognition of old-school algebra techniques, though I didn't really stick to all of the old rules.
Oh damn.
I was just about to pull out one of the other masks in my closet.
Seriously I have about 5 different choices
Quote: beachbumbabsQuote: WizardI've been waiting for an answer to my cannonball problem since April 20. Maybe I need to go back to something a bit easier. That said, here is your next math problem. Winners of a beer within the last year are on a 24 hour hold.
The sum of the current ages of Nathan and Axel is 49. Nathan is twice as old as Axel was when Nathan was as old as Axel is now.
How old are Nathan and Axel now?
Please put answers and solutions in spoiler tags. You must show your work for the beer.Nathan is 28 and Axel is 21.
Answer must be divisible by 7 for the ratios to work. When Nathan was 21 (Axel's age now), Axel was 14 (half Nathan's age now ).
28+21 = 49.
(4*7)-7=(3*7)
(3*7)-7=(4*7)/2
I respect the good ol’ intuition. I can hardly decipher the question.
Current ages: Nathan =X Axel =Y
1. The sum of the current ages of Nathan and Axel is 49.
X+Y = 49
2. When Nathan was as old as Axel is now:
That was (X-Y) years ago, Nathan was Y years old and Axel was Y-(X-Y) = 2Y-X
3. Nathan is currently twice as old as Axel was when Nathan was as old as Axel is now.
So X =2*(2Y-X) = 4y-2X: or X= 4/3 Y
4. Since from step 1, Y = 49-X, and from step 3: X=4/3 Y
X = 4/3 * (49-X)= 4/3*49 -4/3X
7/3*X = 4/3*49
X= 28
and Y =21.
Quote: DRichI think that is crap.
In 9th grade Algebra we had a test of 10 story problems like this. I was the only one in the class to get 10 out of 10 and the teacher failed me. "You didn't show your work". Sorry, I am smart enough to do these in my head. I am still bitter about it.
That teacher is dead and I am not upset about it.
Maybe Wizard is a little biased because BBB is doing so well with the Jeopardy preliminaries.😀 He's taking a little wind out of her sails.
Quote: DRichI think that is crap.
Oh my! My problem could have easily been solved by trial and error, which I don't have much respect for.
It's an important life skill to be able to explain why your answer is what it is. Sorry, but I take your teacher's side.
Quote: billryanI'll take someone that can intuitively get to the answer over someone who needs pencil and paper to do it.
I will take someone who can explain coherently why their answer is right.
So congrats, Doc, on giving him the formulas he wanted, and everybody else please stand down. Thanks!
Quote: beachbumbabsI was not looking to start an argument with anybody over this.
Nor was I. From the beginning I acknowledged that your answer was correct and was submitted prior to mine. I only made my post in reply to the Wizard's requirement that, "You must show your work for the beer", even though I won't be drinking the beer myself. And then I tried a few feeble jokes about all this -- anybody ever seen a lead balloon?
Quote: beachbumbabsI was not looking to start an argument with anybody over this.
Neither was I. I try to provide a fun math problem, and that one has been around for ages, give a beer, and get "crap" kicked in my face. I'm going to file it under "no good deed goes unpunished" and hopefully move on.
Quote: DRichI think that is crap.
In 9th grade Algebra we had a test of 10 story problems like this. I was the only one in the class to get 10 out of 10 and the teacher failed me. "You didn't show your work". Sorry, I am smart enough to do these in my head. I am still bitter about it.
That teacher is dead and I am not upset about it.
Same here. Teacher said you have to show your work except for super obvious stuff. Okay, fair enough. Lots was super obvious, so I obviously didn’t show work for that. Teacher then said I must’ve been cheating or some hogwash. Don’t remember what the exact resolution was, but pretty much I answered a “complicated” problem by doing it mentally and yeah.
TBH, they weren’t even that hard of problems. Like bruh if you can’t just mentally figure out the LCD, GCD, or whatever those numbers are (roots maybe?) in your head then you probably shouldn’t be in that math class.
Although I think she was just salty because I always did my homework and tests in pen. Sacrebleu!
I had been writing/typing for years and my teacher kept insisting I always keep my head tilted to the left with my eyes on papers I was supposed to copy from.
Even glancing back and forth to the keyboard I was doing 80 or 90 words a minute.
She kept telling me she was trying to teach me the proper way to type.
Hell no, she was trying to teach me to be an office secretary. I am dead certain Stephen King and Ernest Hemingway did not write their novels with their heads pointing left towards the wall
Quote: darkozI pretty much failed typing class even though I typed faster than all the other students.
I had been writing/typing for years and my teacher kept insisting I always keep my head tilted to the left with my eyes on papers I was supposed to copy from.
Even glancing back and forth to the keyboard I was doing 80 or 90 words a minute.
She kept telling me she was trying to teach me the proper way to type.
Hell no, she was trying to teach me to be an office secretary. I am dead certain Stephen King and Ernest Hemingway did not write their novels with their heads pointing left towards the wall
That is so funny. Same happened to me. 8th grade typing class on a typewriter. RS you know what one of those are, right? Anyways, I was typing 80 wpm with no errors and by far the fastest in the class but got a C because my hands were not in correct spot. I refused to change and I still type the same way at about the same speed. I remember that year well. It was the same year that I got an F in gym that almost caused me to not graduate
Quote: darkozI am dead certain Stephen King and Ernest Hemingway did not write their novels with their heads pointing left towards the wall
How do you know?
Sphere packing problems are among the most complicated questions that can be asked, no wonder you're not getting an answer. This one may have enough information to be easier than the general question of optimal sphere packing. Numberphile has a great episode on multi dimensional sphere packing. I like the question and hope someone gives did it go.Quote: WizardI've been waiting for an answer to my cannonball problem since April 20. Maybe I need to go back to something a bit easier.
Quote: teliotSphere packing problems are among the most complicated questions that can be asked
I have an answer ready to go. The hard part, I thought, was finding the ratio of the volume of a sphere to the tetrahedron it is inscribed in, which was already solved.
Quote: WizardHow do you know?
Maybe I dont know.
Found this early photo of Stephen King at a typewriter.
But are you sure there is not a more efficient way to pack the spheres into the tetrahedron, that will let you pack more spheres than the pattern you give, for a sufficiently small sphere? That's the rub.Quote: WizardI have an answer ready to go. The hard part, I thought, was finding the ratio of the volume of a sphere to the tetrahedron it is inscribed in, which was already solved.
If you ask for the ratio for a specific pattern, then that's one question. If you ask for the optimal ratio, given unlimited choice in how the spheres can be packed, that's an entirely different and much tougher question.
Quote: teliotBut are you sure there is not a more efficient way to pack the spheres into the tetrahedron, that will let you pack more spheres than the pattern you give, for a sufficiently small sphere? That's the rub.
If you ask for the ratio for a specific pattern, then that's one question. If you ask for the optimal ratio, given unlimited choice in how the spheres can be packed, that's an entirely different and much tougher question.
I'm only asking for the wasted space in a tetrahedron pyramid of infinite size. That problem has remained unsolved here since April 20. However, you posting a video to the solution kind of ruins it.
That video is not a solution to your problem. And I used spoiler tags. The video is about the classical general problem of sphere packing, not the constrained version you posted. I mean, sphere packing was the 18th Hilbert problem, right?Quote: WizardI'm only asking for the wasted space in a tetrahedron pyramid of infinite size. That problem has remained unsolved here since April 20. However, you posting a video to the solution kind of ruins it.
Oh well.
Quote: teliotThat video is not a solution to your problem. And I used spoiler tags. The video is about the classical general problem of sphere packing, not the constrained version you posted. I mean, sphere packing was the 18th Hilbert problem, right?
Oh well.
That video specifically has the answer at the 10:44 point. Oh well. Thanks for ruining it.
First, it is in the spoiler tags so it is not ruined any more than anyone here could go to Google and find the answer for themselves. Second, what's your problem? Why are you going after me for using spoiler tags? I mean isn't that what people used on here for years when they provide answers?Quote: WizardThat video specifically has the answer at the 10:44 point. Oh well. Thanks for ruining it.
I personally think fully solving sphere packing is one of the true miracles of mathematical reasoning in the 20th century. Your version is cute, but the full scope of the question is grandiose and pointing out that your little problem is part of a much bigger problem seems relevant, even if in spoiler tags.
Mike, this kind of irrational attack is so unlike you, all I can say is I hope you're okay.
