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There were a number of solutions that came
in and here are those that had some extra information about how
they went about it.
Shendy
First, I used letters to show the amount of liquid in each
bucket.
R= The amount of liquid in the red basket.
B= The amount of liquid in the blue basket.
Y= The amount of liquid in the yellow basket.
One of the sentences states that:
Y$\div2 = 2$R
Multiply both sides by $2$.
Y$=4$R
As Y must be smaller or equal to $5$, R can only be $1$
So, the red bucket contains $1$ litre of liquid.
Y$=4$R
Y$=4\times1$
Y$=4$
The yellow bucket contains $4$ litres of liquid.
Also, $x$ is the amount of liquid poured from bucket A
As the amount of liquid in bucket B plus the amount of liquid
poured from bucket A equals to the amount of water in bucket
C,
B$+x=5$
As the red bucket contains only $1$ litre of water, $x$ can only
equal to $1$
So,
B$+1=4$
B$=4-1 =3$
The blue bucket contains $3$ litres of liquid.
Jemima, Jasmine, Stephen and Olly used a trial
and improvement approach:
red $1$ litre, blue $3$ litres, yellow $4$ litres
We tried yellow as $5$ litres and that didn't work because you're
not allowed half litres.
But if yellow was $4$ and red was $1$ plus blue as $3$ it would
work because if red was poured into blue it would make $4$ like
yellow and twice the amount in red is $2$ and half of $4$ (yellow)
is $2$.
From Ania:
Let the volume of liquid in the red bucket be N.
Let the volume of liquid in the blue bucket be P.
Let the volume of liquid in the yellow bucket be Q.
N, P and Q are given to be whole numbers.
Each volume is less than $5$ litres, therefore N, P, Q are less or
equal to $5$ (litres).
We are also given:
N+P=Q and $\frac{1}{2}\times$Q$=2\times$N
Re-arranging the last equation we get Q$=4\times$N
As Q cannot be bigger than $5$ and both Q and N are whole numbers
we must take
N$=1$ (if N$=2$ than Q$=8$, which is too much!)
Therefore Q$=4\times$N$=4\times1=4$
As P=Q-N we get P$=4-1=3$
So, the red bucket contains $1$ litre, the blue bucket contains
$3$ litres and the yellow bucket contains $4$ litres.
From Nur:
Because half the liquid in the yellow bucket is the same as
twice that in the red bucket, this means that there is a quarter of
the amount in the red compared to the yellow.
Since they must be whole numbers and they can't be bigger than
$5$, there must be $1$ litre in the red and $4$ in the
yellow.
So then the blue bucket must have $3$ litres.
Finally, a solution that came in right at the
end of the month from Ollie
I was working systematically. First I did the red bucket as $1L$,
the blue bucket as $2L$ and the yellow bucket as $3L$. $1L$ add
$2L$ equals $3L$ so that's ok but half of $3L$ equals $1.5L$ and
$1$ times $2$ isn't $1.5L$ so I knew that was wrong so I went on to
the next one. The red bucket is $1L$, the blue bucket is $3L$ and
the yellow bucket is $4L$. I saw that $1L$ add $3L$ equals $4L$.
And $4L$ divided by $2$ equals $2L$ and $1L$ add $1L$ equals $2L$,
so I knew it was right. That's how I solved thiis problem.
Well done all of you and others who sent in
the correct solution as well. I hope that those of you who did not
send anything in but worked on it enjoyed the thinking that was
necessary.