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Question

There were 5/7 as many red marbles as blue marbles in a jar. Dave took some blue marbles out of the jar and replaced them with the same number of red marbles. The number of red marbles become 5/9 of all the marbles in the jar. Which of the following is a possible number of blue marbles that were replaced.
1) 9
2) 10
3) 36
4) 63
Answer is 2
Why?
Tks

Answer

Marbles must be counted in whole numbers, yes? Good.

So initially, there are 5 red marbles out of every (5 red + 7 blue = 12) marbles.
No matter how many marbles, the number of red marbles is a multiple of 5.

Then we switch around, now there are 5 red marbles out of every 9 marbles.
No matter how many marbles, the number of red marbles is still a multiple of 5.

So the number of blue marbles we switched into red marbles is a multiple of 5.

Hence answer must be 2) 10.

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