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

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): You can put this solution on YOUR website!

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

RELATED QUESTIONS
There were 5/7 as many red marbles as blue marbles in a jar. Dave took some blue marbles... (answered by josgarithmetic,Edwin McCravy,greenestamps)

A jar has twice as many red marbles as white marbles and the ratio of blue marbles to... (answered by Boreal)

there are 300 marbles in a jar that contains only blue and red marbles. the number of... (answered by rm29924)

A jar has twice as many red marbles as white marbles and the ratio of blue marbles to... (answered by scott8148,stanbon)

Jason has the same number of red and of blue marbles. He puts them in two jars so that... (answered by richwmiller)

The ratio of blue marbles to red marbles in a jar is 13 to 5. If there were a total of... (answered by rfer,checkley77)

There are a combined total of 60 marbles in the jar consisting of red, green, blue and... (answered by Fombitz)

A jar contains a total of 20 red, black and blue marbles. There are two more black... (answered by Fombitz)

A jar contains 5 red, 9 blue, and 6 green marbles. What is the probability of selecting... (answered by Fombitz)