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 Post subject: Tricky maths questions
PostPosted: Mon Jul 11, 2016 9:30 pm 
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I have been tearing my hair out trying to work out this question, which everyone else would probably find easy!
It suddenly struck me that I could ask the good people on this forum who are always swift to come to people's aid.

Rambling over... question:

Ben is 3 years older than his sister and a third of the age oh his mother. His father is 4 years older than his mother and four times the age of his sister. How old is Ben???

arrrrrrhggh!!


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PostPosted: Mon Jul 11, 2016 9:37 pm 
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I usually try to draw questions like that - would start with writing down initials and arrows between them to make it easier to see how the relationships work, so e.g. S----->+3----->B for 'Ben is 3 years older than his sister' etc. With this particular one, you could arrange all four people in a shape of a square, with each corner being an initial of a person and arrows showing age relationships between them. All you need to do then is to see who is the person that you can link everyone's age to. I hope this helps. :)

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Last edited by PurpleDuck on Mon Jul 11, 2016 9:44 pm, edited 1 time in total.

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PostPosted: Mon Jul 11, 2016 9:44 pm 
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PurpleDuck wrote:
I usually try to draw questions like that - would start with writing down initials and arrows between them to make it easier to see how the relationships work, so e.g. S----->+3----->B for 'Ben is 3 years older than his sister' etc. With this particular one, you could arrange all four people in a shape of a square, with each corner being an initial of a person and arrows showing age relationships between them.


hi purpleDuck, thanks for replying....

will try but i' sure i won't get the answer.

Previously, I tried sister's age as "x"

so Ben = 3 + x = 1/3 of mum's age (say "y")
then dad is 4 = y
dad is also 4x (4 times sister)

that's as far i could go without knowing how to substitute!


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PostPosted: Mon Jul 11, 2016 9:46 pm 
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OK, try this (you don't need formal algebra/substitution to do it):

S+3=B and Bx3=M and M+4=D
at the same time, we know that Sx4=D

Can you see where I am going with this?

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PostPosted: Mon Jul 11, 2016 9:55 pm 
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i can,.... but i just can't see what the next step is. i'm so glad this is anon - very embarrassing!!


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PostPosted: Mon Jul 11, 2016 9:57 pm 
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Try finding a multiple of 4 which is also a multiple of 3 (so could be mum's age), then look to see whether adding another 4 (for dad's age) gives you a number which is four times the number which is three years less than the number which is a third of mum's age. Not explaining this very clearly :lol:

Possible age for Ben: 1 ... ... 6
Possible age for mum (B*3): 3 ... ... 18
Possible age for dad (M+4): 7 ... ... 22
Possible age for sis (D/4): (7/4) ... (22/4)

Obviously, the ages one is looking for are a bit higher. Also can't get things to line up very well, but hint, think KS3, KS4 ages.

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PostPosted: Mon Jul 11, 2016 9:57 pm 
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Algebra is notoriously difficult with age questions.

Quote:
Ben is 3 years older than his sister and a third of the age of his mother. His father is 4 years older than his mother and four times the age of his sister. How old is Ben???


Try a few ages for Ben's mum as it must be a multiple of 3 and 4 [because of what it says about Dad's age].

No need to try 12 or 24 ... too young

Mum 36 so Ben 12 and sister 9 so Dad 36 x does not work

Mum 48 so Ben 16 and sister 13 so Dad 52 which works ... [4 more than Mum]


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PostPosted: Mon Jul 11, 2016 10:00 pm 
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Guest55 wrote:
Algebra is notoriously difficult with age questions.

Quote:
Ben is 3 years older than his sister and a third of the age of his mother. His father is 4 years older than his mother and four times the age of his sister. How old is Ben???


Try a few ages for Ben's mum as it must be a multiple of 3 and 4 [because of what it says about Dad's age].

No need to try 12 or 24 ... too young

Mum 36 so Ben 12 and sister 9 so Dad 36 x does not work

Mum 48 so Ben 16 and sister 13 so Dad 52 which works ... [4 more than Mum]


Ooh, I was trying to be good and not actually post the answer :lol:

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PostPosted: Mon Jul 11, 2016 10:03 pm 
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As the previous hints had not helped I decided to break my rule about answers. :lol:


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PostPosted: Mon Jul 11, 2016 10:07 pm 
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as this DP was being so thick you had no choice :lol:

i feel for the poor kids who have to learn this at the tender age of 10!

thanks so much all.

i am too ashamed to say my answers came out at 7, 21 and 25 :lol:


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