Combined ages question

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MCLC
Posts: 335
Joined: Sat Jan 09, 2016 6:45 pm

Combined ages question

Post by MCLC »

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?
Guest55
Posts: 16254
Joined: Mon Feb 12, 2007 2:21 pm

Re: Combined ages question

Post by Guest55 »

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.
salsa
Posts: 2686
Joined: Tue Sep 03, 2013 10:59 am

Re: Combined ages question

Post by salsa »

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!
MCLC
Posts: 335
Joined: Sat Jan 09, 2016 6:45 pm

Re: Combined ages question

Post by MCLC »

Thanks both.

Salsa - would you mind asking your husband how he would work it out? Curious to see the other possibilities also. Thank you!
J50
Posts: 296
Joined: Wed Oct 10, 2012 10:35 am

Re: Combined ages question

Post by J50 »

Guest55 wrote:
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]
Guest55
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Joined: Mon Feb 12, 2007 2:21 pm

Re: Combined ages question

Post by Guest55 »

J50 - there is no need for any algebra here - see my post :)
salsa
Posts: 2686
Joined: Tue Sep 03, 2013 10:59 am

Re: Combined ages question

Post by salsa »

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
MCLC
Posts: 335
Joined: Sat Jan 09, 2016 6:45 pm

Re: Combined ages question

Post by MCLC »

Thanks all! Now I understand it :)
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