SOLUTION: 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 mar
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-> SOLUTION: 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 mar
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Question 1206890: 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
Problem with answer choices Answer by greenestamps(13200) (Show Source):
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.
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.
After the change, the number of red marbles was 5/9 of the total number:
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.
Only one of the answer choices is a multiple of 5.
ANSWER: 2) 10
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
