I think this is the nub. I don’t interpret “two times more than” to mean “200% more than”. I interpret it (in the context of the phrasing in the OP, at least) as “greater than, by a factor of 2”. Likewise, I would interpret “two times less than” to mean “less than, by a factor of 2”, i.e., one half.
In fact, I would be willing to bet that that’s the most common interpretation. (The poll results seem to support that.) I have never heard anyone actually say “X times bigger than Y” in a way that meant Y + XY. (I have heard people say “X% bigger than Y” to mean that.)
It’s possible this is, as dracoi suggested, a regional variation. I’m in the midwest, and I don’t think I’ve ever heard anyone use the language in a way that would make 12 the intended answer.
In real life, people are wildly imprecise about numbers, so I’d take someone saying “X times more than” to mean that one thing is noticeably more than the other.
But it’s not real life, it’s a math problem. And as people upthread have said, in the language of word problems “X more than” means to add, "X times as much as " means to multiply, and “X times more than” means to multiply then add.
The answer to the problem in the OP is 12. I can see a case for 8, but it’s not a strong one. 6 is just wrong for the question if it’s phrased as it is in the OP.
This is a very weird attitude. Isn’t the point of word problems to learn to apply math in real life situations? It shouldn’t be a game, decoding a trick that only appears to be something meaningful or useful.
It IS a weird attitude. The standard I have elucidated applies in real life, too. And woe to the advertiser who tries to palm off a six-ounce candy bar as weighing two times more than a three-ounce candy bar.
No, that’s not the point of word problems. In real life, the information given would be “Mary ran 4 laps; John ran 12 laps.”
I use math all the time and I never run into situations that resemble a word problem. No one has ever said to me “This field is three times as long as it is wide, and has a perimeter of 48. What is its surface area?” I’ve never had to guess what coins someone was holding based on a random set of clues. I don’t think I’ve ever cared that two trains leave their stations at the same time traveling at different speeds nor wondered where they’d cross paths. And I did, I’d look at the train tables. Word problems are about figuring out how to apply those words to the math principles being taught that day.
So, you’ve never been responsible for turfing a field, or any similar project of area coverage (shingles, paint, carpet). You’ve never had to arrange a meeting point for people leaving from different places at different times? Never had to divide two pies among five people with the minimum of clean cuts?
Not necessarily! Suppose they started running together, went around a few times, and only then, when Mary took a break, did John start paying attention to his own laps. Then he knocks off. “I went around the track two more times. How many did we do together?”
Seriously, I’m having a hard time understanding how a normal adult could be getting by without at least minor instances of such real-world math-in-words coming up routinely.
Yes - but I’ve been given (or measured) the actual dimensions, not perimeter & weird context clues, or some of the other ways I had to figure out area in word problems.
Of course, but I do it by asking the people “can you be at X meeting point at 8? Great.” I have a specific place in mind. I do not do it by first figuring out where they were, knowing that Bob travels at 20mph, Sally travels at 30 mph, and Jack travels at 25mph NS but 35 mph EW and calculating that they’ll all intersect on 3rd & elm at 7:23. In real life, I don’t want to go to 3rd & elm.
Hell no. No one wants a funky shaped piece of pie and it’s impossible to get it out of the pie pan that way. I cut it in wedges as God intended. Is this something that really happen to you?
I’m not arguing against math. As I said in the previous post, I use arithmetic all the time. I use basic algebra & more complex math often enough. But no, not as things appear in word problems.
How do you divide two pies among five people with the minimum of clean cuts? (ETA: Are radius cuts permitted, or only bisecting cuts?)
For me, in my old profession, “word problems” came up all the time, in the allotment of resources. We’ve got 300 users, all of whom want total database access. (Well, okay, that one’s easy. “No!”) We’ve got users, who want to submit batch jobs, which will take x, y, and z time to run, and which can be submitted with m, n, and o priority, as backed up by a, b, and c levels of managerial authority. It starts to resemble the “box packing” problem more than anything else.
(Hey, when the V.P. of Finance demands a total inventory, he gets it!)
I don’t know if this is the best way to explain it. I finally figured out that it could be twelve when I realized people interpreted Mary’s “time” as four laps. If John ran 2 more “times” that are each also 4 laps, then you get 12.
I’d have voted for 12, but I’ll concede that this is a “purist” interpretation – in a typical conversation I’d guess that 8 was intended, not 12.
“Twice” is interchangeable with the phrase “two times.” (Are there any exceptions?) In many contexts, “once” means “one time.”
If you’ve ordered drinks in a bar and drunk them, you catch the waitress’ eye and say “Once more.” Is the waitress going to bring you drinks, or is she waiting for you to say “Twice more”? :rolleyes:
Those claiming 8 is the answer seem to think that “once more” and “twice more” are synonyms.
Simple… pies are always cut into either 6 or 8 pieces, depending on the size of the pie. People take pieces at will until there is only one left, because it’s impolite to take the last one.
But that’s definitely not the answer your teacher expected to see on a math test.
Assuming the pies are the same kind, three radius cuts per pan. Four people get one 2/5 piece each, one person gets two 1/5 pieces. Take out the small pieces first, that gives you room to get a spatula under one big piece per pan. The pans go with the last big pieces.
Take the pies out of the pans and line the pies up. The first cut is going to be along the bottom of both pies - taking off the bottom 20% (along the chord that goes with a central angle of about 120). One person gets those two pieces. Then line up the cut edges and, in one cut, bisect the two remaining large pieces to make 4 pieces. Each of the remaining people gets one of those.
If I’m not allowed to cut two pies at the same time, 4 cuts, two for each pie.
In real life - I go with dracoi’s solution.
