On Radio 2, apparently, but also reported locally as it's a Cambridge pupil. Ten year old was given the following for homework, got stumped, and rang in.
Is this too hard for you? Took me longer than it should (about ten minutes, blimey!), and of course, you COULD cheat and look up the answer but that wouldn't be any fun.
Off you go.
"I'm a bit stuck says Anna can anyone else do this? Eight grapefruit, seven oranges and three lemons weigh the same as three oranges, six grapefruit and six lemons. One grapefruit weighs two thirds as much as a lemon. A dozen oranges weigh 3 kilograms. How much does a lemon weigh? Excuse me?"
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Took me close to ten minutes too. Not done simultaneous equations for ages, not helped by the fact that I wrote it out wrong thanks to the order of the variables changing in the question.
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Blimey that does seem a bit tricky for a ten year old, I certainly don't remember doing simultaneous equations at junior school in the 67-72 period.
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>> How much does a lemon weigh?
Google gives several answers.
approximately 3 to 4 ounces
Around 150 grams
58 grams (approx 2 ounces)
Well, 99.9% of kids these days have smart phones, and presumably they'll do a web search for the answer ;0
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There is of course, no correct answer. No two lemons weigh the same. Had there been one lemon in the equation it would have been possible to work it out. The correct question should have been of course, "what is the average weight of a lemon as used in the representative quantity of fruits"
And you lot think you should join the pedants club?
Last edited by: Zero on Wed 11 Feb 15 at 09:57
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600g.
Are you sure about the question. "One grapefruit weighs two thirds as much as a lemon." Seriously?
8g + 7o +3L = 3o + 6g + 6L
Eliminating items that appear on both sides
2g + 4o = 3L [This is not sensible. Three lemons do not in the real world weigh the same as seven large fruit: four oranges plus two grapefruit!]
Also, g = 2/3L, so substituting for g
4/3L + 4o = 3L
And 12o = 3kg so 4o = 1kg, so putting all the lemons on the right and substituting kg for o
1kg = [3-(4/3)]L
1kg = 5/3L
L = 600g
That seems crazily heavy, so check by substituting back into the original equation:
16/3L + 3L + 7o = 3o +12/3L + 6L
3.2kg + 1.8kg + 1.75kg = .75kg + 2.4kg + 3.6kg
6.75 = 6.75
Somebody here is getting 600g too. 90 seconds to do the calculation, twenty minutes to check, recheck and then google to see if anybody else gets a silly answer, and then to post all my workings.
www.cambridge-news.co.uk/Radio-2-listeners-asked-help-solve-Cambridge-10/story-26003482-detail/story.html
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Thanks for doing that, MM - didn't mean for you take so much time and effort over it.
Glad you did though, as my answer was two potatoes and a carrot until I checked my workings against yours.
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3/14 of a kg per lemon done in my head in about 60 seconds.
Dunno if it's right though.
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Got a pen and paper and indeed wasn't right - is 600g like everyone else said :-)
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I wonder if the 10 year old was confused because the lemons are bigger than grapefruit?
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My thought too. So I instantly dismissed the question as badly framed:)
Last edited by: NortonES2 on Wed 11 Feb 15 at 15:28
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Possibly framed that way to stop kids going home and putting lemons on mum's kitchen scales, while still using objects kids can picture rather than the 3x+2y+z sort of approach we remember from school.
Difficult bit was trying to do it in my head while on the M40 in traffic yesterday evening, not a good idea only lasted about 5 seconds before I gave up.
Only took a minute or so when I could give some time to it at lunchtime, but then I am not 10.
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If you're going to set questions that use real-life objects then the answers have to make sense. One spends one's entire life trying to make sure that answers make sense; to start out telling a ten-year-old child that a lemon is bigger than a grapefruit is just surreal.
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Indeed, although the idea of knowing the order of magnitude was arguably more important with log tables and slide rules.
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" to start out telling a ten-year-old child that a lemon is bigger than a grapefruit is just surreal."
The state of maturity of the fruits is not stated; maybe they were particularly large lemons and rather immature grapefruit. This was also a splendid test of ability to think laterally as well ;-)
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Thank you, Cliff, we are now starting to see who, on the forum, is capable of lateral thought ;-)
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Ruddy hell, you'd need a lot of gin for that.
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6m30s to get and check what turns out to be the same answer as MM - and with the same misgivings about the relative sizes. Making these things realistic does matter; I keep thinking of Douglas Adams's 'Due to a tragic miscalculation of scale, the entire invasion fleet was accidentally swallowed by a small dog'.
It does seem like quite a complex problem for primary school. I'll ask the Beestlings when I get home.
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Two to three minutes gave me 600gm
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Wouldn't really know where to start with something like this, although I've never found maths of any great interest. Like others on here I found what stuck out was the lemon was so much larger than the grapefruit :-).
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Surely it would be easier to put the lemon on the scales?
Pat
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>> Surely it would be easier to put the lemon on the scales?
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>> Pat
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Isn't it time you went to work?
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one equation with 3 variables, one with 2 and one with 1
So really 2 equations with 2 variables, about a minute to solve with a piece of paper.
simples really.
Orange is 1/4kg, substitute into the other two and eliminate the grapefruit.
The question is a good one as it challenges understanding rather than rote learning. As one of our professors explained to us at University many years ago, if all you needed was a good memory in the exams all the Chinese students would get firsts, the exams were delibarately set to test understanding of the concepts and application of them to new situations.
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Which must be why, although everything up till then was a single beam analysis, the first year mechanical engineering exam I did used a three bladed helicopter. So the weight supported by a single rotor blade was a third of the total.
Some folk certainly got this wrong too, I remember hearing the smacked foreheads as we left the examination hall.
You had to do a bit of mechanical engineering to get an electrical engineering degree. A somewhat hated subject.
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I liked the story of the test given to a class of eight year oldS. The rubric said "read every question before starting".
Those that dived in anyway and ignored that boring italicised stuff at the beginning did all three pages of the test. Those that read everything first read the last page, which said "you do not need to take this test. Go off and play quietly outside but don't tell your classmates why".
Half the class had fun, and the other half learned, hopefully, a valuable lesson.
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A long time ago I didn't read the first page of a mathematics exam. It said something like choose 3 out of 5 questions to answer. I did them all. I was best at maths in the class and saw friends who'd finished.... I hadn't. I was perplexed.
I just managed it all and got top marks. But I'd done 5 out of 5 questions. Doh.
Last edited by: rtj70 on Fri 13 Feb 15 at 22:36
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Too hard for a ten year old? - Fursty Ferret
