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Alvin and Bob had a total of 60 marbles. Alvin gave 1/4 of his marbles to Bob. Bob then gave 1/3 of the total number of marbles he had to Alvin. In the end, each of them had the same number of marbles. How many marbles did Alvin have at first?

By the way, we cannot use algebra to solve this question.

Because this is a primary school(5th Grade) question in Singapore, we can't use algebra to solve since they haven't learnt it.

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Hint: Work backwards. At the end Alvin and Bob have 30 marbles each. Since, Bob gave away 1/3, 30 marbles amounted to 2/3 of what he had originally. And so on...

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At the end each had 30 marbles. Bob must have had 45 at the previous step, to give 1/3 (or 15) marbles to Alvin; at that time Alvin must have had 15 marbles. At the previous step Alvin must have had 20 marbles, to give away 1/4 (or 5) marbles to Bob. Hence at the beginning Alvin had 20 marbles and Bob 40.

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