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Monday, September 25 2017 @ 10:19 AM CDT
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  P6 Hokkien Huay Kuan Prelims 2012 Math Q15
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By: Tping (offline)  Wednesday, July 17 2013 @ 11:13 PM CDT (Read 1166 times)  
Tping

Hi, please help..

Cindy, Dick and Eddy had $410 altogether.
Cindy gave 1/3 of her money to Eddy.
Dick then gave 2/5 of his money to Cindy.
As a result, Dick had $20 less than Cindy and $30 less than Eddy.
How much money had Cindy at first?

Thank you in advance.

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By: echeewh (offline)  Thursday, July 18 2013 @ 04:39 AM CDT  
echeewh

Hi <Tping>,

Following is my worked solution:

This question makes use of <Unchanged Total> concept and <Work Backwards> method.

<Unchanged Total> concept means that at the end the total amount that C, D and E had is the same as what they had at first.


*** - for alignment purpose.

<After>

C |------<-20->| ***** -
D |------| ************** | --> $410 (C+D+E)
E |------<-20-><10>| -


3u --> 410 - 20 - 30 = 360
1u --> 360 ÷ 3 = 120

C: 1u + 20 --> 120 + 20 = $140
D: 1u --> $120
E: 1u + 30 --> 120 + 30 = $150

Use <Work Backwards> method,

<D gave (2/5) of his money to C>
(3/5)D = $120
(5/5)D = 120 × (5/3) = $200

C: 140 - 80 = $60

<C gave (1/3) to E>
(2/3)C = $60
(3/3)C = 60 × (3/2) = $90

E: 150 - 30 = $120

C (at first) = $90

=========

Trust this helps.

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

Cheers,
Edward

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