Let me offer another perspective and method to solve Question 2!
I have seen these particular questions with the same concept tested over the years but I believe most teachers in schools tend not to present it well enough for students.
Here is a method I have come out with and it uses a diagram that allows it to be easier for students to grasp after reading my explanation. I call this the ‘Circle Diagram’ and I teach this to all my students. Happy to share it here with all!
So in that question, let’s imagine that Mr. Teo is going to place all the empty bags in a circle.. How many bags are there? Right now, we do not know, but let’s first move on to find out.
Moving on, now with all the bags in a circle, Mr. Teo is going to place 4 oranges into each bag. After making one full round with the bags, and now with each bag having 4 oranges, Mr. Teo has 3 extra oranges with him, keep this in mind, it is important for later on.
Mr. Teo now decides to go for a second round to distribute oranges into all these bags. We still do not know how many bags there are, but, let’s move on first…
We learn that the question says “if he packs 5 oranges into each bag, there will be short of 4“.
Since there are already 4 oragnes in each bag, Mr. Teo has to place only 1 additional orange into each bag. He has 3 extra oranges, remember? He will be able to only place 1 additional orange into the first 3 bags. And the rest of the bags will not have the extra orange.
In order to ensure that all the bags in the circle have an extra orange, Mr. Teo will need to get 4 more. That tells us that there are only 4 more bags ahead that need those extra oranges each (in order for Mr. Teo to complete a second round of distribution to all bags) .
So, from this we can observe that there are 3 bags with the extra orange, and 4 bags without the extra orange. We now know that there are 7 bags in total!
Now that we know there are 7 bags, we can calculate the number of oranges Mr. Teo actually has. This is shown in my working on the last segment.
Hope this helps everyone to see this question in another perspective!
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