This blog is managed by Song Hock Chye, author of Improve Your Thinking Skills in Maths (P1-P3 series), which is published and distributed by EPH.

Monday, April 21, 2008

Nanyang Primary School P5 SA2 2006

Posted by Anonymous 21 Apr 2008 PM 01:48
Nanyang Primary SchoolSA2 2006 Primary 5

Three girls shared a sum of money. Cathy received $180 more than Betty. The total amount Betty and Cathy received was 3 times the amount Alice received. The amount Alice and Cathy received was 5 times the amount Betty received. What was the sum of money shared by the three girls?

pls enlighten. thanks

(As time does not permit, please note that this will be my last post in response to requests from the public. I will however still post worked solutions from my own database and requests from my own students)

Cathy received $180 (3 groups of $60) more than Betty.
Betty and Cathy received 3 times the amount Alicia received.

Betty + Cathy ----- 6 units + 3 groups of $60

Alicia has one third of that -----
(6 units)/3 + (3 groups of $60)/3
= 2 units + $60

At the same time, Alice and Cathy received 5 times the amount Betty received. Therefore, Betty’s amount has to be multiplied 5 times to be equal to the total of amount of Alice and Cathy.

Betty x 5 ----- Alicia + Cathy
(3 units x 5) ----- (2 units + $60) + (3 units + $180)
15 units ----- 5 units + $240
10 units ----- $240
1 unit ----- $24

Total sum of money -----
8 units + $240
= (8 x $24) + $240
= $192 + $240 = $432

Answer: $432


Anonymous said...
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Excel Eduservice said...

Please do not spam. It won't be nice for me to report your IP address to Google and have your account suspended.

keentolearn said...

Dear Mr. Song

Thank You for your very informative blog. It certainly provides a useful platform for P5 and PSLE students.

Judging from some comments, there may be some readers who found your answers long, difficult and confusing. Unfortunately, they did not take the trouble to elaborate on the areas where are having problems.

One important point to note is that Mr. Song’s answers focus on explaining the concepts and mechanics which strengthen a student’s skill in answering Maths questions. If students just memorise steps without much understanding, they’ll face difficulties if they encounter similar problems with some tweaks in the future.His blog is targeted at average and above average students, which explains why his answers are more elaborate.

Your blog is certainly a must read for upper primary students. However, nothing is perfect in life; the challenge is to continuously seek improvement. On this point, perhaps, those having troubles understanding the answers should write to express the areas they are having difficulties, so that future answers may be further refined for the benefits of all students.

Mr. Song, we appreciate your efforts. A big Thank You.

Excel Eduservice said...


What I post in this blog is what I teach in class. My teaching method does not differ. This has been my method even when I was teaching in schools years back. It must be remembered that face-to-face teaching has some benefits blogs do not have.

One of them is real time feedback from students. Hence, in class, I know exactly where a student has difficulty immediately. I can re-explain on the spot and move on from there.

For blogging, I cannot identify the exact problem area a particular student (or parent) may have in understanding my method. Hence, my written explanation has to be based on my past experience, where I believe students have problems, then tailor my written explanation to address those common problems.

However, in doing that, the written explanation will not solve the “odd problem” which a particular student may face, which others may not.

Another point to note is that when students learn in a classroom environment, there is also verbal explanation. I cannot do that on blogs (unless I post a video which is going to be even more time consuming).

Since blogging lacks audio explanation, I have to fill those “blanks” with written explanation. This means students (and parents) have to read a longer text.

Learning through visual and audio (in class) is definitely more effective than learning through visual only (through blogs). As such, some students may feel it is more difficult to learn strategies from blogs.

Much as I would like to simplify my explanation further than what I have done in this blog, there are restrictions. If I cut the text short, I leave “gaps”. If I explain in too much detail, the length of the text looks visually intimidating to students.

Students and parents should remember that Maths should be learnt in the class with a teacher/tutor explaining its concept and methods.

Blogging can NEVER replace the class teacher.

Excel Eduservice said...

Alfiah, try this

Question - Three girls shared a sum of money.

1. Cathy received $180 more than Betty.

2. The total amount Betty and Cathy received was 3 times the amount Alice received.

3. The amount Alice and Cathy received was 5 times the amount Betty received.

What was the sum of money shared by the three girls?

Explanation –

1. In the model, Cathy has to have $180 more. (3 x $60 = $180)

2. Since Betty and Cathy have an amount 3 times the amount Alice has, Alice will have 1/3 of the amount of money Betty and Cathy have. So divide that sum (Betty and Cathy) by 3 to get Alice’s model.

3. Since Alice and Cathy’s amount is 5 times the amount of Betty’s, you need to have 5 of Betty’s amount to match the other 2 girls’ amount. Therefore, Betty’s amount needs to be multiplied by 5.

Hope that helps.

Student said...

I could'nt understand the explanation. Sorry...

Observer said...

To student:

I have tried to redraw the model. Hopefully this could help you to understand better.

Check it out at
(PSLE Maths: Maths-Whole Number)

Observer said...

Hi student,

Someone has proposed to continue with the model drawing for the last part.

I have also made use of Ratio Method to solve this.

They are posted at Maths-Whole Number.