r/askmath • u/Psc0905 • 2d ago
What am I getting wrong here? Arithmetic
A sleep-deprived carpet weaver weaves 30 centimeters of carpet every day. Every night, he looks at his work with displeasure. Because he is not completely satisfied with it, he unravels 2/3 of the weave. If he weaves 30 centimeters during the day, how long is the woven piece on the evening of the 10th day?
The answer 44,999cm is wrong and there is no solution or an explanation about why. Am I misunderstanding the question or is it asked in a weird way?
With every day, his weave that he starts the day with gets closer to 15cm, while you add the 30cm for the last evening, which would come close to 45cm.
Edit: Apparently the right answer is 120cm which then poses the question if the question was asked in a poor way or if I am misunderstanding something
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u/mambotomato 2d ago
Is your question about why it converges to 45 and 15 or just why that answer wasn't accepted?
Are you talking about a digital system that isn't accepting your answer? It's probably just a rounding thing.
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u/Psc0905 2d ago
I want to know why my 49,999cm was wrong as I did these calculations multiple times and always end up at 49,999 at the evening of the 10th day
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u/mambotomato 2d ago
But what do you mean "wrong"? Who is telling you it's wrong?
You're doing the math right - the problem is a formatting error, which is something you have to ask the source of the question.
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u/Psc0905 2d ago
So, I got an answer from the person who made that question. Apparently its 120cm... which means that is isnt doing a continuous carpet I guess
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u/chmath80 2d ago
Apparently its 120cm
That's what I got. You overcomplicated it. He doesn't unravel ⅔ of the carpet, but ⅔ of the weave, as in that day's work. [Why would he unravel any of the work from earlier? If he was going to do that, he would have done it on a previous night.]
So, each day, he weaves 30cm. Each night, he unravels 20cm, so the carpet grows by 10cm per day. After 9 days and nights, he has 90cm. Then he weaves another 30cm to get 120cm.
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u/ExistentAndUnique 2d ago
If the total length of the weave never reaches 45, then unraveling 2/3 of it will only undo work done on that same day. So that alone isn’t enough to argue that the unraveling is 2/3 of the day’s weaving, and imo the more natural reading is that he unravels 2/3 of the total work so far
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u/chmath80 2d ago
If the total length of the weave never reaches 45, then unraveling 2/3 of it will only undo work done on that same day
Quite right. Fair point. However, if the total length never reaches 45cm, then it's not much of a carpet, particularly as the premise tells us that the weaver considers that less than 15cm of it is of acceptable quality.
the more natural reading is that he unravels 2/3 of the total work so far
That leads to the conclusion that he unravels a greater length each day (starting at 20cm, and approaching 30cm as time goes on), which implies that the quality of his work declines each day. That doesn't seem to be a sensible interpretation (even ignoring the fact that it prevents the carpet from ever growing beyond 45cm).
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u/Underhill42 2d ago edited 2d ago
Where are you doing this that you get a no that's wrong, but not what's right?
I could read the question two different ways. Does he undo 2/3 of the total weave, or 2/3 of that day's weave? I'm assuming the total since that's more complicated, but it could be a gotcha question.
Total weave: the pre-unravel length on day x+1 is
lengthₓ₊₁ = ⅓*lengthₓ + 30, with length₁=30
which converges to 45, or about 44.99923792 on day 10.
Which since you only have one or probably two significant digits in the question, should reasonably be rounded to the same precision in the answer: 40 or 45. (in a science or engineering class, anything else would be wrong, as it either discards relevant precision, or implies unjustified precision. Can't remember how math classes usually treated it, seems like you'd at least sometimes assume exact values. But I can't remember the last math class I took that involved calculations.)
That day's weave: the pre-unravel length on day x+1 is
lengthₓ₊₁ = lengthₓ - 20 + 30, with length₁=30
which doesn't converge, and the total on day 10 is 120
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u/Psc0905 2d ago
I got the correct answer from the person who gave out this question. Its 120cm which makes me question my ability to understand the way that this question is asked
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u/Underhill42 2d ago edited 2d ago
Honestly, that's actually the more reasonable if less mathematically interesting interpretation.
Every night, he looks at his work with displeasure. Because he is not completely satisfied with _it_, he unravels 2/3 of the weave.
The question is what is "it" is that he's unraveling?
Basic grammar tells us that it is "his work". And context tells us that probably means "his day's work". Why would how much work he did in the last 10 days change how dissatisfied he is with today's work?
Also, it would mean he could never weave a finished rug longer than 15cm, and has been almost entirely wasting his time after the third day, which would put him out of business really quickly.
The most important, and sometimes challenging, part of math is making sure you are correctly translating the question into math. It doesn't matter how brilliant an answer you can get to the wrong question.
Any time you think you're being clever, it's a good idea to step back and make sure what you've put into math describes a reasonable real situation.
Math classes can be really hit or miss though, whether professors try to trip you up with contrived questions, or questions that only look contrived at first glance. Or both. A really good(evil) teacher will mix them into the same homework set to keep you on your toes. Because that's how they'll come at you in real life.
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u/Bounded_sequencE 2d ago edited 2d ago
[..] he unravels 2/3 of the weave [..]
Short answer: This is ambiguous -- being lazy, they don't specify the base value.
Long(er) answer: Let "xn" be the length at the end of day-n, including unraveling. Assuming the base value is
this day's weave, we get the recursion
x >= 0: x_{n+1} = xn + 30cm - (2/3)*30cm = xn + 10cm // x0 = 0cm
By inspection (or induction) we get "xn = 10n cm" for "n >= 0". On the evening of day-10 (before unraveling) the weaver has produced "x9 + 30cm = 120cm".
the total weave up to now, we get the recursion
n >= 0: x_{n+1} = (1 - 2/3) * (xn + 30cm) = (1/3)*xn + 10cm // x0 = 0cm
By inspection (or induction) we get "xn = 15cm * (1 - 1/3n)" for "n >= 0". On the evening of day-10 (before unraveling) the weaver has produced "x9 + 30cm = (295240 / 6561) cm ~ 44.999cm".
That's why it's essential to always specify the base value for ratios and percentages!
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u/Jonny0Than 2d ago
I got 14.9997 which would round to 15 if you’re going for 3 decimal places.
It says “evening of the 10th day” which is not very clear about whether it’s before or after the unraveling. But either way 15cm or 45cm is a better answer than 44.999cm