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 Post subject: Combined ages question
PostPosted: Sat Jan 16, 2016 6:49 pm 
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Joined: Sat Jan 09, 2016 5:45 pm
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Hi can someone help with the following:

The combined age of Alan and Ben is forty three.
The combined age of Alan and Carl is fifty five and the combined age of Ben and Carl is sixty-six.

What is the combined age of Alan, Ben and Carl?

How old is Alan?


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PostPosted: Sat Jan 16, 2016 6:52 pm 
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Joined: Mon Feb 12, 2007 1:21 pm
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Quote:
The combined age of Alan and Ben is forty three.
The combined age of Alan and Carl is fifty five and the combined age of Ben and Carl is sixty-six.


If you think about these three facts and add them then you have ....

Let me know if the hint isn't enough to get the first part - once you know that then Alan's age should be straight forward.


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PostPosted: Sat Jan 16, 2016 8:19 pm 
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I added Alan and Carl (55) plus Ben and Carl (66) total 121
Then substracted Alan and Ben (43) as we had them included in the sum above:
Total 78 which is Carl's age twice, so I divided it by 2 = 39
So, Carl is 39, then you can deduct 39 from Alan and Carl's age to get Alan's = 16
Alan is 16.
You know that Ben and Carl is 66, so add 16 and you get 82 for the three.

I bet there are quicker ways of doing it and the reason I mostly leave Maths to my husband who works these problems out very quickly!


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PostPosted: Sat Jan 16, 2016 9:25 pm 
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Thanks both.

Salsa - would you mind asking your husband how he would work it out? Curious to see the other possibilities also. Thank you!


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PostPosted: Sat Jan 16, 2016 9:41 pm 
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Guest55 wrote:
Quote:
The combined age of Alan and Ben is forty three.
The combined age of Alan and Carl is fifty five and the combined age of Ben and Carl is sixty-six.


If you think about these three facts and add them then you have ....

Let me know if the hint isn't enough to get the first part - once you know that then Alan's age should be straight forward.



Yes, this is the easy way.

A+B+A+C+B+C = 43+55+66

so you basically have 2x the combined ages 2(A+B+C) = 164 etc. and easy to get A from that

[v. similar question at the end of Kingston Grammar's maths paper last year]


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PostPosted: Sat Jan 16, 2016 9:45 pm 
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J50 - there is no need for any algebra here - see my post :)


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PostPosted: Sat Jan 16, 2016 9:51 pm 
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Joined: Tue Sep 03, 2013 9:59 am
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Ok. He did it differently and quicker.
To know the age of the three. Add all the ages and divide by two. This as you have all the ages twice.
2a+2b+2c=164
A+b+C= 82
82- (b+c) = a
82-66=16


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PostPosted: Sun Jan 17, 2016 2:52 pm 
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Thanks all! Now I understand it :)


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