Question 1206870
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Note that it is hard to know how to answer the question, since you didn't provide the answer choices.<br>
But we can do some analysis to determine what kind of answers are possible.<br>
Initially the number of red marbles was 5/7 the number of blue marbles.  That means that the red marbles were 5/12 of the total and the blue marbles were 7/12 of the total.<br>
Let x be the total number of marbles.  Then (5/12)x is the original number of red marbles.
Let y be the number of blue marbles that were removed and replaced with red marbles.<br>
After the change, the number of red marbles was 5/9 of the total number:<br>
{{{(5/12)x+y=(5/9)x}}}
{{{y=(5/9)x-(5/12)x=(20/36)x-(15/36)x=(5/36)x}}}<br>
x and y are whole numbers.  Since y=(5/36)x, the total number of marbles must be a multiple of 36, and the number of blue marbles that were removed and replaced with red marbles must be a multiple of 5.<br>
There is not enough information to find a single possible answer for the number of blue marbles that were removed and replaced with red marbles.  But we do know that...<br>
ANSWER: any number that is a multiple of 5<br>
Some possible sets of numbers for the problem....<br>
36 total marbles; originally 15 red and 21 blue; 5 marbles changed to give 20 red and 16 blue; 20/(20+16) = 20/36 = 5/9<br>
72 total; originally 30 and 42; 10 change to give 40 and 32; 40/(40+32) = 40/72 = 5/9<br>
etc....<br>