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 P6 2011 SA1 CBS
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By: JessicaTan (offline)  Tuesday, April 30 2013 @ 10:26 PM CDT (Read 648 times)  
JessicaTan

Please help with working solution.

Fahim & Ron had a total of 120 stickers at first. In the first game they played, Fahim lost 1/4 of his stickers to Ron. In the second game they played, Ron lost 3/8 of his stickers to Fahim. As a result, both have the same number of stickers left. How many stickers did each of them have at first?

(answer key : Fahim 32, Ron 88)

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By: echeewh (offline)  Thursday, May 02 2013 @ 05:51 PM CDT  
echeewh

Hi Jessica,

Following pls find my worked solution:


This is a typical example of Internal Transfer concept where total number of stickers at first remains unchanged in the end. (Unchanged Total). Observe that the process is about stickers being lost from one person to the other.

Hence, total number of stickers in the end was 120.

Applying <Work Backwards> method {since both F,R have same number of stickers left}, we have ...

<After 2nd Game>
F: 60
R: 60

<Process1>
R: Lost (3/8) of his stickers to F.
(5/8) R = 60
(8/8) R = 60 × (8/5) = 96
R had 96 stickers before 2nd game; infers that R lost 36 stickers {96 - 60} to F.
F: 60 - 36 = 24

<After 1st Game>
F: 24
R: 96

<Process2>
F: Lost (1/4) of his stickers to R.
(3/4) F = 24
(4/4) F = 24 × (4/3) = 32
F had 32 stickers before 1st game; infers that F lost 8 stickers {32 - 24} to R.
R: 96 - 8 = 88

<At first>
F: 32
R: 88

========

Trust this helps.

Do let me know again if there's further clarification.

Cheers,
Edward

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