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Tuesday, December 12 2017 @ 07:49 PM CST
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 Raffles Girls Prelim 2011 Q16
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By: echeewh (offline)  Friday, June 22 2012 @ 06:11 PM CDT (Read 962 times)  
echeewh

Hey AngCH

This is to provide the worked solution to your above question :

Question:
There were 225 apples and 253 oranges in Box A.
There were 260 apples and 212 oranges in Box B.
Mr Chia moved some apples and oranges from Box B to Box A.
In the end, 40% of the fruits in Box A and 70% of the fruits in Box B were apples. How many fruits did Mr Chia move from Box B to Box A?

--------------------------------------------------------

Worked Solution:

(***) - buffer for alignment purpose

<After>
Box A********Box B
A : R********* A : R
40 : 60*******70 : 30
2 : 3**********7 : 3

Applying <Unchanged Total> concept, we have ...
Apples (A) in A,B remain unchanged <Before> and <After> and,
Oranges (R) in A,B remain unchanged <Before> and <After>.

Hence,

2p + 7u --> 225 + 260 = 485 --- (1)
3p + 3u --> 253 + 212 = 465 --- (2)

Eliminating (p):
(1)x3:
6p + 21u --> 1455 --- (3)
(2)x2:
6p + 6u --> 930 --- (4)

(3)-(4):
21u - 6u --> 1445 - 930 = 525
15u --> 525
1u --> 35

Substitute 1u into (2):
3p + (3 x 35) --> 465
3p --> 465 - 105 = 360
1p --> 120

<Before>
Number of fruits in B = 260 + 212 = 472
<After>
Number of fruits in A = 5p --> 5 x 120 = 600
Number of fruits in B = 10u --> 10 x 35 = 350

Number of fruits moved from B to A = 472 - 350 = 122

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

Trust the above helps.

Cheers,
Edward

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Registered: 04/21/11
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