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 Henry Park P6 2011 SA1 Paper 2 Q14
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By: kyChang (offline)  Friday, May 25 2012 @ 12:47 AM CDT (Read 970 times)  
kyChang

Pleas help ;p

There are two bags of jelly beans labelled A & B. In bag A, there are 470 red jelly beans and 480 green jelly beans.
In bag B, there are 350 red jelly beans and 200 green jelly beans. Some red and green jelly beans from bags B are transferred
to bag A. As a result, 60% of the jelly beans in bag A and 20% of those in bag B are red. How many red and how many green
jelly beans are transferred from bag B to bag A?

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By: echeewh (offline)  Sunday, May 27 2012 @ 10:30 PM CDT  
echeewh

Hi there,
Following pls find worked solution:

<Before>
Bag A
RA : GA
470 : 480


Bag B
RB : GB
350 : 200


<Process>
R and G jelly beans transferred from Bag B to A

<After>
Bag A
RA : GA
60 : 40
3 : 2 5p

Bag B
RB : GB
20 : 80
1 : 4 5u

<using Unchanged Total concept>, we have ...
(i) After Total (RA + RB ) = Before Total (RA + RB )
(ii) After Total (GA + GB ) = Before Total (GA + GB )

(i)
3p + 1u --> 470 + 350
3p + 1u --> 820 --- (1)

(ii)
2p + 4u --> 480 + 200
2p + 4u --> 680 --- (2)

Given that we need to find the number of R and G jellybeans transferred from Bag B, we shall find the number of jellybeans remaining in Bag B. (i.e. find 1u qty while eliminating (p) ).

Hence, applying Simultaneous / Compare & Replace technique, we eliminate (p) as follows:

(1)x2:
6p + 2u --> 1640 --- (3)
(2)x3:
6p + 12u --> 2040 --- (4)

(4)-(3):
12u - 2u --> 2040 - 1640
10u --> 400
1u --> 40

Bag B <After>
1u (R) --> 1 x 40 = 40
4u (G) --> 4 x 40 = 160

Number of R jellybeans transferred from B to A
= 350 - 40 = 310

Number of G jellybeans transferred from B to A
= 200 - 160 = 40

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

Trust this helps.

Cheers,
Edward

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