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By: 2000123 (offline)  Monday, April 16 2012 @ 03:56 AM CDT (Read 1040 times)  
2000123

2/7 of Danny's marbles were green and the rest were sliver.He gave away 21 sliver marbles and bought another 12 green marbles.He then had the same number of sliver and green marbles.How many sliver marbles did he have at first?

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By: echeewh (offline)  Monday, April 16 2012 @ 05:53 AM CDT  
echeewh

Hi there,

Pls find the following solution:

Note: * - used to buffer up the whitespace..

Since 2/7 were Green (G), then 5/7 were Silver (S). Hence ratio becomes ...

*****G : S
*****2 : 5

+ 12G - 21S

*****1 : 1

12 G were added; 21 S given away; Number of G = Number of S so ratio becomes 1 : 1.

Next step, you can use either Model Method ( work backwards) , Cross-Multiply or SImultaneous methods. If you are not familiar with the latter 2 methods, then the Model method ( work backwards ) will do for this one.

<After>
G |---------------|
S |---------------|

( Working backwards means that in order to arrive to the Before model, you need to reduce 12 for G and increase 21 for S; and that will give you the initial proportion or ratio of 2 : 5 )

<Before>

*************12
***********|<----|
G |---------------|
****<-2u->

*******************21
*****************----->|
S |---------------|
***<--------5u--------->

By comparing the G and S models now and applying the Gap & Difference technique, Gap = 12 + 21 while the Diff ( in units ) = 5u - 2u = 3u. We have....

3u ---> 33
1u ---> 11

Number of S marbles at first = 5u ---> 5 x 11 = 55.

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

Trust the above solution helps.

Cheers,
Edward

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By: 2000123 (offline)  Monday, April 16 2012 @ 07:38 AM CDT  
2000123

thanks

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