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I always find these 2 types of questions similar but need to know whether it is the same way to solve them.  I can do question 1 but not sure about 2

  1. Aini and Usha each had a piece of dough of the same mass for making buns.  The same mass of dough was used for each bun.  Aini made 40 buns and had 50g of dough left.  Lisha made 10 buns and had 1.1 kg of dough left.  a) what was the mass of dough needed for each bun?     b) With the remaining dough from both girls, how many more such buns can be made at most?


2.  Miss Seow wants to give some chocolates to her pupils.  If she gives each pupil 5 chocolates, she will have 128 chocolates left.  If she gives each pupil 13 chocolates, she will have 40 chocolates left.  How many pupils are there?


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This type of question also very similar .  But cannot use the method above :

When a stack of books are packed in bags of 4, there would be 3 books left over.  When a stack of books are packed in bags of 6, there would be 3 books left over. What could be the least number of books in the stack?

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Packs of 4:

  4 8 12 16
total 7 11 15 19

Packs of 6:

  6 12 18 24
total 9 15 21 27

So, minimum number is 15.

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This is how i will come out with a solution for the question on Miss Seow her pupils:

For these kind of questions, we don’t really need fancy methods or drawing models to solve. We can solve it logically. Let’s just discuss and picture some scenarios and we will arrive at the answer.. 

Let’s imagine Miss Seow’s group of children seated in a circle and Miss Seow has decided to go one full round around them to distribute some chocolates to them. If she gives each of them 5 chocolates, she will have 128 chocolates left in her paper bag where she keeps the chocolates..

Now, suppose we don’t know how many children are there seated in the circle yet, lets just continue to use some imagination..

Miss Seow now decides to give 13 chocolates each, instead of giving 5. Like it says so in the question “if she gives 5…… then if she gives 13…….” remember that this is if she gives. The thing is, she didn’t actually give.

So let’s get back to the children and Miss Seow. The children already have 5 chocolates in their hand (assuming they havent eaten them yet), and Miss Seow wants them to have 13 each instead of 5, so what Miss Seow will do, is she will make a second round around the children, and give an additional 8 chocolates to each child now, so that 5 + 8 = 13.

After finishing the 2nd round, she realises now that in the paper bag, she has 40 chocolates left. Before distribution in the 2nd round, she had 128, but now she had 40 left. So that means, in the second round, she gave away 128 – 40 = 88 chocolates!

And remember that in the second round she had to give an additional 8? So if she gave away 88 chocolates in the second round and each child received 8, that means that there were 11 children! ( check that 88 divided by 8 is 11)

There we have our answer, no need for models or fancy methods. Hope this helps because as a tutor, we know that more often that not, models do over-complicate things for some questions and they put our students in more confusion than they already are.



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Dear Hayden

Thanks for your in depth explanation.  Very much appreciated.

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you give really great reply and detailed answers Hayden. I appreciate the effort and knowledge that you share here. Keep it up 

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I also noticed that you have posted a 3rd question as well. 

To clarify with you, the 3rd question is not similar at all to the 1st and 2nd question.

Regarding the 3rd question, the best way to solve the question is to do a listing method which has already been done by SavingPrivateTutor.

It is listing out of the multiples of 3 and also the multiples of 6 and then with the list, add on an additional 3 books to the values, as there were 3 books leftover after packing. And after adding 3 to the values, we can see the common value of 15, which fits the criteria in the question.


Hope this helps to clarify the differences in the 3 questions! Feel free to ask more questions by dropping a private message.

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Hi Xueyan

The 2 questions above are not very similar when it comes to solving them and for the methods used. I will try to help you out with these 2 questions originally posted. 

To answer the first question on Aini and Usha:

We see that Usha has made 10 buns, which is 30 fewer buns compared to Aini ( Aini made 40). Because of the 30 fewer buns made by Usha, Usha has managed to use 1050 g less dough than Aini. 1100 g – 50 g = 1050 g.

This tells us that 30 buns require 1050 g of dough. So, 1 bun requires  1050 g ÷ 30 = 35 g.

That is the answer for part a.

To answer part b, 

with the remaining dough, which is 1100 g + 50 g = 1150 g, 

the number of buns that can be made at most will be 1150 g ÷ 35 g = 32.86,

which means it is at most 32 more buns.


Hope this helps, will answer the other question in another post…

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