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 Post subject: Help with a maths question pleasePosted: Wed Oct 10, 2007 8:56 am

Joined: Wed Sep 26, 2007 9:00 am
Posts: 438
Hi,
This one has had me stumped for days I just have a complete mental block.
Could anybody help me with the method for solving please?

In July 2006, Becky was two thirds of Mary's age and half of Anna's age. In July 2011, Becky will be three quarters of Mary's age and three fifths of Anna's age.
How old was Becky in July 2005?

thanks
scatshouse

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 Post subject: Posted: Wed Oct 10, 2007 9:10 am

Joined: Mon Aug 13, 2007 10:47 am
Posts: 3310
Location: Warwickshire.
Right, here goes. Took me a while and not sure if I will explain it properly...
I started off just looking at the relationship between the ages of Becky and mary knowing that initially Becky needs to be two thirds of mary and toyed around with their numbers for July 2006 first of all. Eventually got to 10 for becky and 15 for Mary as this makes Becky two thirds of Mary's age. Then I added 5 years to each of the ages to work out how old they would be in 2011 which would make them 15 and 20.
Now let's add Anna. In 2006 mary was half Anna's age which would make Anna 20 and in 2011 Becky would be three fifths of Anna's age so add 5 years onto Anna - 25 and we all ready thought Becky would be 15 in 2011 and 15 is three fifths of 25.

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 Post subject: Posted: Wed Oct 10, 2007 9:11 am

Joined: Mon Aug 13, 2007 10:47 am
Posts: 3310
Location: Warwickshire.
So Becky would be 9 in 2005 as I subtracted 1 fro her age in 2006.
There, think that's it!!

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 Post subject: Posted: Wed Oct 10, 2007 9:20 am

Joined: Wed Sep 26, 2007 9:00 am
Posts: 438
Doh!
Thanks Ed's mum,
That's so easy when you look at it like that. I was playing around with all the fractions!
No wonder son just walked away!
Thanks
scatshouse.

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 Post subject: Re: Help with a maths question pleasePosted: Wed Oct 10, 2007 9:59 am
scatshouse wrote:
This one has had me stumped for days I just have a complete mental block.
Could anybody help me with the method for solving please?

In July 2006, Becky was two thirds of Mary's age and half of Anna's age. In July 2011, Becky will be three quarters of Mary's age and three fifths of Anna's age.
How old was Becky in July 2005?

It can be done by trial-and-error, but I think this one needs algebra.

Let b, m and a be the ages of the girls in July 2006. Then the first sentence translates as

b = 2/3 m = 1/2 a

In July 2011, their ages will be b+5, m+5 and a+5, so the second sentence translates as

b+5 = 3/4 (m+5) = 3/5 (a+5)

It's enough to consider only two of the girls, say Becky and Anna. (The third is mainly useful as a check.) Substituting a/2 for b in the second equation gives

a/2+5 = 3/5 (a+5)

and solving that gives a = 20 and thus b = 10 and m = 15. And then there's the final trick that you have to subtract 1 to get Becky's age in 2005. After doing a lengthy calculation, so many children forget to go back and check exactly what answer they were asked for.

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 Post subject: Re: Help with a maths question pleasePosted: Wed Oct 10, 2007 10:56 am

Joined: Fri Jul 06, 2007 8:31 pm
Posts: 1245
scatshouse wrote:
Hi,
This one has had me stumped for days I just have a complete mental block.
Could anybody help me with the method for solving please?

In July 2006, Becky was two thirds of Mary's age and half of Anna's age. In July 2011, Becky will be three quarters of Mary's age and three fifths of Anna's age.
How old was Becky in July 2005?

thanks
scatshouse

Horrible Question. My approach is to creep up on the question setter from another angle...

"and three fifths of Anna's age." implies that in 2011 Anna's age is a multiple of 5.

In 2006 Anna's age is divisible by 2. But also must be a multiple of 5 since it's 5 years earlier...

therefore obvious guess is Anna is 20 in 2006 and 25 in 2011.

Plug in the numbers and it works...

(10 and 15 also good candidates... would have tried that next)

Makes B 10 in 2006

I think a question like this would have freaked out DD.... I'll ask her and see what happens...

Regards
SVE

_________________
Animis opibusque parati

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 Post subject: Posted: Wed Oct 10, 2007 3:43 pm
Is this eleven plus maths question?..NFER or SATS

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 Post subject: Posted: Wed Oct 10, 2007 7:13 pm

Joined: Wed Sep 26, 2007 9:00 am
Posts: 438
Hi,

Kenta,
This was from a sample maths paper for the exam for St .Anselm's College, Wirral.
It was, however, the last question in the booklet and maybe the most difficult. (for me anyway!)

Thanks once again,
scatshouse.

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