11 Plus Exams Forum

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?

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.

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!

Thanks both.

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

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]

J50 - there is no need for any algebra here - see my post

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

Thanks all! Now I understand it