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 Post subject: Combined ages questionPosted: Sat Jan 16, 2016 6:49 pm

Joined: Sat Jan 09, 2016 5:45 pm
Posts: 60
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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 Post subject: Re: Combined ages questionPosted: Sat Jan 16, 2016 6:52 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11949
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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 Post subject: Re: Combined ages questionPosted: Sat Jan 16, 2016 8:19 pm

Joined: Tue Sep 03, 2013 9:59 am
Posts: 1662
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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 Post subject: Re: Combined ages questionPosted: Sat Jan 16, 2016 9:25 pm

Joined: Sat Jan 09, 2016 5:45 pm
Posts: 60
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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 Post subject: Re: Combined ages questionPosted: Sat Jan 16, 2016 9:41 pm

Joined: Wed Oct 10, 2012 9:35 am
Posts: 296
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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 Post subject: Re: Combined ages questionPosted: Sat Jan 16, 2016 9:45 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 11949
J50 - there is no need for any algebra here - see my post

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 Post subject: Re: Combined ages questionPosted: Sat Jan 16, 2016 9:51 pm

Joined: Tue Sep 03, 2013 9:59 am
Posts: 1662
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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 Post subject: Re: Combined ages questionPosted: Sun Jan 17, 2016 2:52 pm

Joined: Sat Jan 09, 2016 5:45 pm
Posts: 60
Thanks all! Now I understand it

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