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 P6 Maths! 2012 Prelims Nan Hua Paper 2 Q18
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By: Tping (offline)  Thursday, September 05 2013 @ 09:06 AM CDT (Read 934 times)  
Tping

Hi please help..

Q18)
Kelly and Javier each had a certain sum of money.
If Javier gave Kelly $40, Kelly would have twice as much as Javier.
If Kelly gave Javier $40, Javier would have thrice as much as Kelly.
How much more money did Javier have than Kelly?

Thank you.

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By: echeewh (offline)  Thursday, September 05 2013 @ 10:38 AM CDT  
echeewh

Hi <Tping>,

Following is my worked solution:

*** - for alignment purpose

Both <If> cases are 'internal transfer' processes; hence, we can apply the <Unchanged Total> concept to the ratios of monies left after the transfer / exchange. I.e. the total units of monies of J, K in the two ratios from the two <If> cases are the same.

<If J gave K $40>
J : K ** Total
1 : 2 **** 3 -- (1)

<if K gave J $40>
J : K ** Total
3 : 1 **** 4 -- (2)

Applying <Unchanged Total> concept, multiply (1) 4x, (2) 3x as shown:

<If J gave K $40>
J : K ** Total
4 : 8 *** 12 -- (3)

<if K gave J $40>
J : K ** Total
9 : 3 *** 12 -- (4)

<Before>
from (3), J = 4u + 40 -- (5)
from (4), J = 9u - 40 -- (6)

As (5)=(6), we can equate these.

4u + 40 = 9u - 40
9u - 4u = 40 + 40
5u --> 80
1u --> 16

from (3), K = 8u - 40

Difference in monies between J, K:

J - K = 4u + 40 - (8u - 40)
= 4u + 40 - 8u + 40 = 80 - 4u

80 - 4u --> 80 - (4 × 16) = 80 - 64
= $16


An alternative method that can also be used is the <Simultaneous> method, as shown in my other previous worked solutions.

========

Trust this helps.

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

Cheers,
Edward

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