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PostPosted: Tue Oct 30, 2012 3:54 pm 
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Hi ... I thought I was good at Maths but have had a brain freeze on this one.... Help and explanation gratefully received.

2 pears and 3 oranges cost £1.06
1 pear and 4 oranges cost £1.03

What is the price difference between oranges and pears?

Huge thanks to you mathes whizzes!


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PostPosted: Tue Oct 30, 2012 4:02 pm 
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loveyouradvice wrote:
Hi ... I thought I was good at Maths but have had a brain freeze on this one.... Help and explanation gratefully received.

2 pears and 3 oranges cost £1.06
1 pear and 4 oranges cost £1.03

What is the price difference between oranges and pears?

Huge thanks to you mathes whizzes!


In each situation, you have five pieces of fruit. If you take away a pear and replace it with an orange, you reduce the total price by 3p. Hence, oranges are 3p cheaper than pears.

To confirm (and presumably this would not be expected at 11+), you solve the simultaneous equations to find that oranges are 20p each and pears are 23p each.


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PostPosted: Tue Oct 30, 2012 4:03 pm 
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loveyouradvice wrote:
Hi ... I thought I was good at Maths but have had a brain freeze on this one.... Help and explanation gratefully received.

2 pears and 3 oranges cost £1.06
1 pear and 4 oranges cost £1.03

What is the price difference between oranges and pears?

Huge thanks to you mathes whizzes!


Hmm - try doubling the second one so 2 pears and 8 oranges = £2.06 so 5 oranges would be £1 and 1 orange would be 20p

then if three oranges are 60p 2 pears will be 46p or 23p each ... so is that answer 3p?


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PostPosted: Tue Oct 30, 2012 4:04 pm 
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Joined: Sun Sep 09, 2012 6:32 pm
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loveyouradvice wrote:
Hi ... I thought I was good at Maths but have had a brain freeze on this one.... Help and explanation gratefully received.

2 pears and 3 oranges cost £1.06
1 pear and 4 oranges cost £1.03

What is the price difference between oranges and pears?

Huge thanks to you mathes whizzes!


p is pears, g is oranges

A: 2p + 3g = 106
B: 1p + 4g = 103

2B: 2p + 8g = 206

2B - A: 5g = 100
g = 20

Substitute back in to A:
2p + 3g = 106
2p + 60 = 106
2p = 46
p = 23

Answer: Pears cost 23p, Oranges cost 20p

I hope this makes sense. I've never tried to type it on a computer before.

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The more that you read, the more things you will know.
The more that you learn, the more places you'll go.
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PostPosted: Tue Oct 30, 2012 4:05 pm 
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Oops - I was too slow!

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The more that you read, the more things you will know.
The more that you learn, the more places you'll go.
Dr Seuss


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PostPosted: Tue Oct 30, 2012 5:23 pm 
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JRM wrote:
Answer: Pears cost 23p, Oranges cost 20p


Yes, but it's rare for 11+ exams to explicitly require the solution of simultaneous equations. Note what was asked for: not the prices of the two pieces of fruit, but just the difference. As I said earlier on, you can deduce that the difference is 3p without needing to work out the actual prices, and the prices are substantially harder to solve for.


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PostPosted: Tue Oct 30, 2012 5:26 pm 
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Yes - daveg's solution is the most elegant offered and does exactly what is required.

Just think of the time saved by thinking and not automatically going into algebra which 11+ pupils are certainly NOT intended to use. :D


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PostPosted: Tue Oct 30, 2012 5:48 pm 
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daveg wrote:

To confirm (and presumably this would not be expected at 11+), you solve the simultaneous equations to find that oranges are 20p each and pears are 23p each.



I misread that as 'would be expected at 11+' rather than 'would NOT be expected at 11+' so I just worked it out to prove to myself that it worked. But then as it was just in a forum called Maths and we don't sit a maths 11+ paper here I didn't relate the question to the 11+. That might sound mad given that a month ago I could think of little else, but it is true! And finally, that is how my DS would work it out to confirm his answer.

Anyway, I'm sorry if my use of algebra alarmed anyone. I like daveg's solution, and hopefully this will make me think before I type again. (I'm relieved I got to the right answer though, it would have been even more embarassing had I not :-) )

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The more that you read, the more things you will know.
The more that you learn, the more places you'll go.
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PostPosted: Tue Oct 30, 2012 6:47 pm 
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Joined: Fri Sep 15, 2006 8:51 am
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daveg wrote:

In each situation, you have five pieces of fruit. If you take away a pear and replace it with an orange, you reduce the total price by 3p. Hence, oranges are 3p cheaper than pears.



This is very good and relies on noticing that there are actually the same number of fruits in each half of the equation :roll: -


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PostPosted: Wed Oct 31, 2012 11:57 am 
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What great answers guys - thanks for them all!!!!!!

Yup, gotta remember that there is usually an easy option - espeically if its not one of the tough questions at the end!


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