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 By: anooravi (offline)  Friday, May 02 2008 @ 07:34 PM CDT (Read 2364 times)
anooravi

The following 5 marks problem sum appeared in a CA1 (2008) school paper. I was keen in sharing since the sum at the first glance seems complicated but the solution is simple,provided the students get the right technique. Let them give a try.

After a Math quiz, Mr Li gave the three prize winners some pens to share. The first winner received 1/3 of the total number of pens plus another 2 more pens from the same total. The second winner received 1/3 of the remainder plus another 3 pens. The third winner received 1/3 of the new remainder plus 6 more pens. There was no pen left after this. How many pens were there in all?

Newbie

Registered: 12/31/06
Posts: 12

 By: anooravi (offline)  Monday, May 05 2008 @ 09:56 AM CDT
anooravi

The answer for the problem sum is 30 pens.
This sum is more easier by Model Drawing than by algebra. I am sure all of you would agree with me.

Newbie

Registered: 12/31/06
Posts: 12

 By: graceong (offline)  Tuesday, May 11 2010 @ 09:39 PM CDT
graceong

Your question on Mr Li giving the pens to his prize winners is very intriguing. Care to show by model drawing how this is done?

Newbie

Registered: 04/26/10
Posts: 2

 By: nisalam (offline)  Friday, May 14 2010 @ 07:27 AM CDT
nisalam

last kid had 1/3 + 6 of the new remainder, and there was none left - meaning 6 equals 2/3 of the new remainder. So the new remainder would have been 9 (which is what the 3rd kid received).
2nd kid had 1/3 + 3 of the remainder, meaning what was left for the 3rd kid was 2/3 of the remainder minus 3. So 9 + 3=12 was 2/3 the original remainder. So the second kid had 6 + 3 = 9 pens as well.
The first kid had 1/3 of the original sum + 2, so the original remainder was 2/3 - 2. That amounts to the total of the 2nd and 3rd kid. So 2/3 = 9 + 9 + 2 = 20
Therefore the original number was 30.
If you don't understand this, let me know and I'll try to put up an attachment of the model.

P.S. Thanks @anooravi, for sharing the question!

Junior

Registered: 04/29/10
Posts: 30

 By: graceong (offline)  Sunday, May 16 2010 @ 09:52 PM CDT
graceong

Tks, Nisalam. Took me awhile to figure it out .... but, it's clear. Tks alot. How do you show it by model, though? Would appreciate if you could show it by attachment. Don't you think it's quite a mind twisting exercise for a 12-year-old? My child will face this in two years' time. I tremble for her. But, thanks a lot.

Newbie

Registered: 04/26/10
Posts: 2

 By: nisalam (offline)  Monday, May 17 2010 @ 08:01 AM CDT
nisalam

hmmm, I have a word document ready, but I have a problem uploading it as an attachment (getting the error message that the file type is not allowed). any help on that will be appreciated
but, don't worry, Grace, children are wonderful creatures ... they'll manage somehow.
my own son is in P6 this year; his biggest worry is the dreaded MT, esp as he is taking a language that is not even our own, and he never uses it outside the classroom, sigh.

Junior

Registered: 04/29/10
Posts: 30

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