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PostPosted: Tue Feb 07, 2012 1:39 pm 
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Joined: Fri Feb 18, 2011 1:45 pm
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Hi All,

What is the best way to approach logic questions? For example quesitons like these:

* Alice and her Dad have a total weight of 117kg. Alice and her Mum weigh 88kg between them. Mum and Dad together weigh 161kg. What is the total weight of Mum, Dad and Alice?

* A maths test contains 10 questions. Ten points are given for each correct answer and three points deducted for an incorrect answer. If Ralph scored 61, how many did he get correct?

* A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each



I tend to go via the algebric route. But then that would require my DS to have a clear understanding of the basic principles of algebra. Will it be too hard for a 10 year old to grasp these concepts??

If Algebra is not the right approach, then how else could we make the child understand these problems?

Thanks,
earleymom


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PostPosted: Tue Feb 07, 2012 2:12 pm 
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with my dd I sort of use algebra but write it all out so she can see how it works
Dad+ Alice = 117 Alice +Mum =88 Mum+Dad=161
2dads +2 mums+2 alices= 117+88+161= 366
1dad +1mum +1 alice = 366/2= 183Kg


the second one - 7 right answers would make 70 points and 3 wrong ones would mean deducting 9 = 61
I'll leave the last one for someone else!!


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PostPosted: Tue Feb 07, 2012 2:15 pm 
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Location: Reading
For the first one I think you would need to use algebra:
A + D = 117
A + M = 88
M + D = 161

So A + M + D = ?

I would do the following steps:
Add 1st and 3rd lines to get
A+ M + 2D = 278

Then take away the 2nd line to give
2D = 190
So D = 95

add 2nd line back in
A + M + D = 88 + 95 = 183
No need to work out A or M individually.


For the second one, a number of points ending in a 9 have been lost. The only options for this that divide by 3 are 9 and 39 but there aren't enough questions to have lost 39 points ( or 69 /99 ) so it must have been 9 points lost which is 3 Q wrong so he got 7 right. Logic rather than algebra

The 3rd one is back to algebra
M = W + 4
M = S x 5
6/7 x M = W

this took me a lot of steps sp hoping someone else can show me a quicker way. I wouldn't want DD to get this one in an exam

When S was born
6/7 x M = M - 4
6M = 7M - 28
So M = 28 and W = 24

M= S+28
M = S x 5
I afraid for this I just stepped up till I found a pair that worked as in
28 and 0
29 and 1
Etc till I got to
35 and 7, with M being 31


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PostPosted: Wed Feb 08, 2012 4:25 pm 
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A man is 4 years older than his wife and 5 times as old as his son. When the son was born, the age of the wife was six-sevenths that of her husband's age. Find the age of each

Husband’s age has to be common multiples of 7 (when son was born) and 5 times tables now- so looking at the pattern 28 and 35 works.
He is 28 when son is born, wife was 24- 6/7ths of 28
Now son is 7
Wife is 31
Husband is 35

Didn't use algebra. wouldn't know how to on that one. I think the 6/7th's was the key to unravelling it.


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PostPosted: Wed Feb 08, 2012 8:37 pm 
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Location: Reading
Much simpler - at least the answer was the same :)


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PostPosted: Thu Feb 09, 2012 11:37 am 
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Thanks everyone for the replies..

DC17C - I try to do it your way too(writing the names instead of x an d y).. But I found it hard to explain my DS how
Quote:
1dad +1mum +1 alice = 366/2


Lady Byron - I like your approach, think thats the way to go forward with a 10 year old.. And Reading mum, I did the same as you did for the age problem and it took forever to find the solution.


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PostPosted: Thu Feb 09, 2012 6:00 pm 
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Joined: Wed Oct 12, 2011 8:34 pm
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I suppose break it down a bit more



2 dads + 2 mums + 2 Alice's =366

is the same as 2x (1 Dad + 1Mum + 1 Alice) = 366

so 1x (Dad + Mum + Alice ) is 366 divided by 2= 183


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PostPosted: Mon Feb 27, 2012 10:29 am 
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Alice and her Dad have a total weight of 117kg. Alice and her Mum weigh 88kg between them. Mum and Dad together weigh 161kg. What is the total weight of Mum, Dad and Alice?


its a nice trick if we want to take
2(a+b+c)=117+88+161=366
then (a+b+c)=183
I want to know what is the each one weight?


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PostPosted: Sat Jul 28, 2012 10:17 pm 
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Joined: Wed Jan 18, 2012 11:41 am
Posts: 4605
Location: Essex
Nines Awe wrote:
Alice and her Dad have a total weight of 117kg. Alice and her Mum weigh 88kg between them. Mum and Dad together weigh 161kg. What is the total weight of Mum, Dad and Alice?


its a nice trick if we want to take
2(a+b+c)=117+88+161=366
then (a+b+c)=183
I want to know what is the each one weight?


Actually, once you have spotted that the info given equates to two of each person, that way is much neater, however...

Alice + Dad = 117Kg
Alice + Mum = 88Kg

therefore

Dad is 29Kg (117 - 88) Kg heavier than Mum.

Dad + Mum = 161Kg

therefore

Mum is 66Kg ((161 - 29)/2) and Dad is 95Kg ((66 + 29) or (161 - 66)).

Alice is 22Kg (88 - 66).

Just to check, according to this method the total is 22 + 66 + 95, i.e. 183Kg, as in the (2A+2D+2M)/2 method .

_________________
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