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Losing Marbles Over Question on Marbles

It is back to school and my son is now in P4. The maths, it seems, getting tougher with each year.

So it is the first month of school and the teacher decided to give a maths workshop, which I suspect is to gauge the level of "smartness" in addressing questions.

I look at every maths question as a challenge. Out of the 4 questions, I was initially stumped by the following questions on marbles.

There were twice as many blue marbles as red marbles in a container. After 240 red marbles were removed from the container, the number of blue marbles was thrice the number of remaining red marbles. How many blue marbles were there in the container?

 My initial approach to the question was to go with the first sentence, followed by the next one. This gave me the following block diagram.


That got me stumped. the problem was how do you account for the 240 red marbles that were removed? How do you find the answer then?

I searched the internet and even got an example of ratios. But my son hasn't been taught ratios yet. Applying the ratio approach was also confusing for me.

After leaving the question aside for a day, I decided to scrawl the internet for a similar example. Then I found one.

The approach to solve this problem is to look at the after first and take the first sentence into consideration later. Also, not drawing the lines to break the blocks into 2s or 3s also helped.


After removing the 240 Red marbles, we know that Blue is thrice of Red. So Red is now 1u and Blue is 3u.

When we add the 240 red marbles back, we are told that Red is half of Blue - There were twice as many blue marbles as red marbles in a container.

So this means that the other half of the Blue marbles can be represented by the 1u+240 number of marbles.

Therefore

3u - 1u = 240 + 1u + 240

2u = 480 + 1u

1u = 480

So there are 480 red marbles left after taking over 240 red marbles. And since  the number of blue marbles was thrice the number of remaining red marbles, there are

480 x 3 = 1440 blue marbles.





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