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 Post subject: Maths experts please!
PostPosted: Thu Oct 02, 2008 7:27 pm 
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Joined: Sun Nov 19, 2006 12:48 pm
Posts: 163
Can someone (Guest 55?!) please help with a method for the following question:

1G + 2M = £2.80
2G + 5M = £6.10

Find the value of 1G and 1M.

I'm totally stumped and memories of struggling with maths are flooding back. I've poured myself a glass of wine, but that's not helping!

Any help would be very gratefully received

Jess


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 Post subject:
PostPosted: Thu Oct 02, 2008 7:35 pm 
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Joined: Tue Dec 13, 2005 12:49 pm
Posts: 1647
Location: berkshire
poss..

Dont you multiply one so that tehre is an equal number of one of the unknowns?

ie 1G + 2M = £2.80
times 2 = 2G+4M = £5.60

then take one from the other....

2G + 5M = £6.10 minus 2G+4M = £5.60

leaving

1M = 50p

therefore

1G would be £1.80 (substituting into 1G +2M=£2.80)

maybe...havent checked....check later...something burning in oven :shock:


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 Post subject:
PostPosted: Thu Oct 02, 2008 7:49 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11940
1G + 2M = £2.80
2G + 5M = £6.10 [note there really should NOT be £ signs in the question]

Yes - we need the same number of Gs or Ms so


1G + 2M = £2.80 (x2) 2G + 4M = £5.60
2G + 5M = £6.10 (x1) 2G + 5M = £6.10

so M = £0.50 or 50p


back in our first equation,

1G + 1 = £2.80

so G = £1.80 now check in the other equation: 3.60 + 2.50 does give 6.10 so we are correct! :lol:


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 Post subject:
PostPosted: Thu Oct 02, 2008 7:54 pm 
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Brilliant! Thanks Chad, hope your dinner's not too burned...

How do you explain the principles of this solution to a 10 year old, such that they'd be able to apply the same method to similar questions?


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 Post subject:
PostPosted: Thu Oct 02, 2008 7:56 pm 
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Sorry Guest 55, cross-posted with you

Thanks all


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 Post subject:
PostPosted: Thu Oct 02, 2008 8:04 pm 
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It's year 8 work really - I would not expect to see questions like this.

The usual ones are:

Two cups of tea and a biscuit cost £1.30, a cup of tea and a biscuit cost 80p.

So you can 'see' straight away that the extra cup of tea is 50p.


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 Post subject:
PostPosted: Thu Oct 02, 2008 8:13 pm 
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Location: berkshire
I think the main thing is to show them that they need to get one of the 'unknowns' the same.... ie... 2 lots of 2G..........then it is just taking the smaller amount from the larger amount.

try it with simple sums

ie 1A + 3C = 11
2A + 4C = 16

multiply the first equation by 2 so that you have the same number of A's in both equations.

2A +6C = 22

minus the second one

2A +6C = 22
- 2A + 4C = 16

0 + 2C = 6


giving 2C = 6 therefore C = 3


sorry...... hope you can read this...haven't got the hang of getting them all under each other... :?


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 Post subject:
PostPosted: Fri Oct 03, 2008 8:26 pm 
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Joined: Sun Nov 19, 2006 12:48 pm
Posts: 163
Yes, I can read it and it makes perfect sense...once someone has shown you how to do it. This was always my problem with maths...understanding it once it has been explained is one thing, working it out for yourself is quite another! Thanks very much for your help.

Guest 55-this question is from an independent school 11+ past paper. How they expect a 10/11 year old to be able to work it out I don't know. It's certainly not something that's been covered in the curriculum


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 Post subject:
PostPosted: Fri Oct 03, 2008 8:34 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
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Jess,

Shocking question in my opinion - the units should not be there.

OK I could 'train' someone to do this sort of question but that is not good teaching or effective learning ...


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 Post subject:
PostPosted: Fri Oct 03, 2008 10:21 pm 
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Joined: Tue Jan 01, 2008 1:05 pm
Posts: 515
Guest55 wrote:
1G + 2M = £2.80
2G + 5M = £6.10 [note there really should NOT be £ signs in the question]

Yes - we need the same number of Gs or Ms so


1G + 2M = £2.80 (x2) 2G + 4M = £5.60
2G + 5M = £6.10 (x1) 2G + 5M = £6.10



Or

2G = 5.60 - 4M
2G = 6.10 - 5M

Therefore

5.60 - 4M = 6.10 - 5M
5M - 4M = 6.10 - 5.60

M = 0.50

Might seem convoluted, but may help in theory behind solving equations, and why you can subtract one equation from the other.


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