Question 1206890
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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>
Only one of the answer choices is a multiple of 5.<br>
ANSWER: 2) 10<br>
The 10 blue marbles that were removed and replaced with red marbles are 5/36 of the total number of marbles
So the total number of marbles was 72
Originally the red marbles were 5/12 of the total, so there were 30 red marbles and 42 blue
After the exchange there were 40 red marbles and 32 blue
In the end the red marbles were 40/72 = 5/9 of the total<br>