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 P5 Catholic High SA2 Math Qn 14
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By: RachelAng (offline)  Wednesday, August 15 2012 @ 03:55 AM CDT (Read 717 times)  
RachelAng

Can someone help with the solution to this question:

Aaron and Ben shared a sum of $200. Aaron gave 3/5 of what he has to Ben. Ben later gave 1/5 of what he has back to Aaron. They ended up with equal amount of money. How much did Aaron have at first ?

Thank you very much !

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By: echeewh (offline)  Wednesday, August 15 2012 @ 08:17 PM CDT  
echeewh

Hey rachel,

Following pls find my worked solution ( Work Backwards method ).

Start from where A,B had equal amount of money

<after>

A: |---------------|
B: |---------------|

<process>
Working backwards, B gave (1/5) to A, and left with (4/5). So divide B into 4p; likewise for A. Add back 1p to B, while removing 1p from A. So B --> 5p, A --> 3p.

A: |--|--|--|
B: |--|--|--|--|--|

A gave (3/5) to B, and left with (2/5). Divide the 3p of A into 6u (i.e. 1p --> 2u). So A --> 6u; Likewise, B --> 5p x 2 = 10u. As (2/5) --> 6u, (5/5) --> 15u. So add back 9u to A, while remove 9u from B. So A --> 15u, B --> 1u.

Hence, the <before> model is as follows:

*** - buffer space for alignment purpose

***<------ 15u ------>
A: |--|--|--|--|--|--|--|-|
B: |-|

Given A,B shared a total sum of $200 at first, we have ...

16u --> 200
1u --> 12.50

A (at first) = 15u --> 15 x 12.50 = $187.50

===========================

Trust this helps.

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

Cheers,
Edward

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