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Khai Han
Posts:
1
From:
Singapore
Registered:
11/6/08


Bases and apples.
Posted:
Nov 6, 2008 2:11 AM


Hi all. I'm new here. Hope you guys can clarify my question.
In this following story, b6 means base 6: i.e. 123b6 = 1x6^2 + 2x6^1 + 3x6^0 and all answers should be in base 6.
An old man wanted to divide 3104b6 of his apples equally among his 5b6 grandchildren and he would contribute as many apples needed so that no apples remained.
(i) How many apples did each of his grandchildren get? (ii) How many apples did the elderly contribute?
I've worked out the total numbers of apples to be 688b10. And after dividing, each grandchild gets 137b10 = 350b6. That settles the first one.
The second one is simple right? 688b10  (137b10 x 5) = 3b10 which is the remainder. But the answer from my tutor is 2b6.
His working is:
3104b6 / 5b6 = 345b6 r 3b6 [I get this one.]
3104b6 = 345b6 x 5b6 + 3b6 [I get this one too.]
+2 3104b6 = 5b6 x (345b6 + 1b6)
I don't get the rationale from the last one. I have a feeling i misunderstood the question when it says that he 'contributes' because prior to this question people gave him a lot of apples (2175 of em). Not sure what he did but somehow he got a remainder.
So what does it mean by 'contribute'?
Does that mean the old man gives 2 more to the grandchildren so that everyone gets the same?
Wait. That makes sense now.



