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 Post subject: Another ratio question!
PostPosted: Sun Dec 06, 2015 10:40 am 
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Joined: Wed Oct 14, 2015 1:24 pm
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Can anyone help with how to approach this type of question?

In a zoo, 1 ape is worth 6 baboons; 4 baboons are worth 5 crocodiles; 3 crocodiles are worth 2 dingoes, and 5 dingoes are worth 4 eagles.

1) Which of the animals is worth the least?

2) How many eagles are worth 1 ape?

Thanks so much!


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PostPosted: Sun Dec 06, 2015 10:55 am 
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I'd start by trying to get a number common to all - I looked at:

1 ape = 6 baboons (x 10)
10 apes = 60 baboons

then you can find other equivalences ... does that help? I'll post more detail if you need it.


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PostPosted: Sun Dec 06, 2015 11:28 am 
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That's a fiendish question!

Using x by 10's seems easy but am stuck on where to go from there!


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PostPosted: Sun Dec 06, 2015 11:38 am 
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Once you know what 60 baboons are you can find how many crocs that it and so on ...


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PostPosted: Sun Dec 06, 2015 11:56 am 
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Location: Chelmsford and pleased
I drew it with bars.


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PostPosted: Sun Dec 06, 2015 12:45 pm 
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Times the first group by 4, then the second group by 6 so you have the same number of baboons in both groups. Then keep going.


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PostPosted: Mon Dec 07, 2015 5:14 pm 
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Thank you very much for the help! I think we've worked it out now.


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PostPosted: Mon Dec 07, 2015 9:36 pm 
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Sounds a bit like an Independent School entrance exam final scholarship question

Algebraic substitution would be the natural way to work this out with expressions for 1a

Thus

1a=6b (given) substituting for c gives
1a= 6 x 5c/4= 7.5c and for d gives
1a= 7.5x 2d/3= 5d and for e gives
1a=5 x 4e/5= 4e

Hence b=(1/6)a
c= (1/7.5)a
d= (1/5)a
e=(1/4)a

so c is the least (smallest fraction) and 4e=a

It's interesting that I don't think Algebra is in KS2 yet (is that correct G55?) but the scholarship type questions in Independent entrance exams usually require a reason knowledge of Algebra to answer quickly

As an aside, this was the final Maths question in an old Solihull School (Independent) Maths Paper:-

Quote:
T is a town on the shore of a large lake, and various boats and hovercraft stop at T in their journeys around the lake. The total distance round the lake is 180 kilometres.

At 10:00am a boat starts from T and travels clockwise round the lake at a speed of 15kph. At the same time a hovercroft starts from T and travels round the lake in the opposite direction at 60kpm.

(1) How far has the boat travelled by the time the hovercraft gets back to T?

(2) When do the hovercraft and the boat meet each other?

(3) How far has each vessel travelled when they meet?


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PostPosted: Mon Dec 07, 2015 9:48 pm 
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My method took less than a minute with no algebra needed.

Algebraic expressions are in KS2 but not solving equations:

Year 6 Algebra:
* use simple formulae
* generate and describe linear number sequences
* express missing number problems algebraically
* find pairs of numbers that satisfy an equation involving two unknowns.
* enumerate all possibilities of combinations of two variables.


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PostPosted: Mon Dec 07, 2015 9:49 pm 
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Joined: Mon Jun 18, 2007 2:32 pm
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Location: East Kent
Quote:
t's interesting that I don't think Algebra is in KS2 yet


yes, it is now

It is formally introduced in year 6, but as G55 says, algebraic thinking can be incouraged earlier on

I like these,

https://nrich.maths.org/10941


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