NB Homework

DavidofMersea

DavidofMersea

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My 7 year old Granddaughter came home yesterday with this homework question.

Jim and George want to buy a chocolate bar. Jim needs 2p more and George needs 50p more, and together they don't have enough to buy the chocolate bar - How much is the chocolate bar?

We (her parents and I) have worked this out by trail and error, but how should this be calculated.

My 7 year old Granddaughter has no idea

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jim+george<chocbar
jim+2=chocbar
george+50=chocbar

jim=chocbar-2
george=chocbar-50

jim+george<chocbar
(chocbar-2)+(chocbar-50)<chocbar (substitute)
-2+chocbar-50<0 (take chocbar from both sides)
chocbar<52 (add 52 to both sides)

chocbar=george+50
chocbar-50=george (take 50 from both sides)
chocbar-50>=0 (george must have >= no money)
chocbar>=50 (add 50)

chocbar must be 50 or 51


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Substitute for P in P=J 2 and P=G 50 and check that J G is less than P.Using Excel you get the following.

Price Jim George sum J G
50 48 0 48
51 49 1 50
52 50 2 52

Assuming George had some money "George needs 50p more" then price is 51p.

Well what else can you do on a dark, wet and windy morning.

I see that the table format changes when shown on the forum so shunt the headings and numbers into 4 separtate columns.
<hr width=100% size=1><P ID="edit"><FONT SIZE=-1>Edited by johna on 23/10/2004 09:28 (server time).</FONT></P>
 
Excuse me for asking David but is your site name derived in a similar way to JesusofNazereth or OhmyGod.
Roy

<hr width=100% size=1><A target="_blank" HREF=http://colvicownersclub.mysite.wanadoo-members.co.uk>http://colvicownersclub.mysite.wanadoo-members.co.uk</A>
 
Choc bar =Jim +2
Choc bar = George + 50 : George +50 = Jim + 2 or Jim = George + 48
George + Jim + x = Choc bar
George + George + 48 + x = Choc bar = George + 50
x = George + 50 - 2 George - 48
Choc Bar = 2George + 48 + George + 50 - 2 George - 48

Bored yet?

Me too so I go with 50 or 51p as the correct answers too. Both work so your granddaughter should include them both for extra marks :)
Complex algebraic equations are really a bit too much for 7 year old!!!

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Are you sure that you are doing the right thing.
Problems now with homework for a 7 year old could become pretty demanding by the time she is needing help with coursework for GCSE.
And the morality of it all ?
Ken

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I must say that I was surprised at the standard of the question, however I don't see this as a problem.

This is not easy, but nor is life. I never had any homework from school, either junior or senior, and when I left I was very immature, and incapable of looking after myself. I used to watch TV every evening.

Although only 7 years old, Georgia is very mature I can take her to grown up events and places, without her being a pain in the backside, and being an embarrassment to me.

Don't imagine that Georgia is sitting at home sweating over her studies all evening. Georgia has a very full and active life, and practises gymnastics five evenings a week, she goes swimming, canoing, sailing etc. She enjoys life and is happy to do all these things and there is no pressure from us. How much better than just watching TV? I bought her an Optimist last week

When she grows up, I expect that she will be very mature, although she is that now, and she will be able to cope with life's problems.





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Seven year olds wouldn't solve this algebraically, they would use number scales - long strips of paper with numbers marked on. The problem then becomes very simple.


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I instictively would have used the algebra method. However, if you think about it logically it is fairly straightforward.

If Jim only needs another 2p to buy the chocolate bar and together they don't have enough, then George has less than 2p, i.e. 1p or no money at all. If he has no money then the chocolate bar is 50p, if he has 1p then the chocolate bar is 51p.

On the basis that it doesn't indicate that George has no money at all, the answer would be 51p.

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Taken probably from this site, as it's one of Octobers questions. The site is run by University of Cambridge, and is a mathematics resource site for students and teachers. You can see the ranking level this question has been given

<A target="_blank" HREF=http://nrich.maths.org/public/viewer.php?obj_id=2416>http://nrich.maths.org/public/viewer.php?obj_id=2416</A>

<hr width=100% size=1>Me transmitte sursum, caledoni
 
Has anyone read the question properly?

Together they have 52p which is not enough to buy one bar between them.

So the answer is simply more than 52p

<hr width=100% size=1>David
 
Presumably they are having trouble recruiting. This is the 'problem of the week'

...It has been estimated that the mass of insects caught by spiders in a year in the UK is equal to the mass of the human population of the UK. Assuming this population is 60 million and the average mass of a human is 70 kg, what is the mass, in tonnes, of insects caught by spiders per year in the UK?
Duh?

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Re: Has anyone read the question properly?

Ah the old verbal reasoning. It always catches mathematicians out.

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I should correct myself

I said in the post above "They have 52p between them" I should have said they "Need 52p more between them"



<hr width=100% size=1>David<P ID="edit"><FONT SIZE=-1>Edited by david on 24/10/2004 23:05 (server time).</FONT></P>
 
The Full Answer

They need another 52p betwwen them

So how much do they have?

Jim only needed 2p so he has 50p
George needed 50p so he has 2p

So between them they have 52p

The 52p they have + the 52p they need = £1.04p

So the price of the choccy bar is £1.04p

<hr width=100% size=1>David
 
Re: Has anyone read the question properly?

They don't have 52p between them - it is a very cleverly worded question as you assume that they do.

Jim needs 2p more (he actually has 49p already)
George needsd 50p more (he actually has 1p already)

The bar costs 51p and between them they only have 50p this solution satisfies all the criteria in the question. There is also a 50p solution (i.e Jim has 48p now and george has nothing).

Any solution with the bar costing less than 50p is impossible -as george would have to have a negative amount of money. Any solution above 53p won't meet the "and together they don't have enough to buy the chocolate bar " requirement

i.e for 53 p solution Jim would need to have 51p now and george would have to have3p now which means that between them they would have 54p which is enough to buy it.
For your 1.04 solution, Jim would have 1.02 and george would have 54p which means that between them they have 1.56 - more than the price of the bar.

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