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.

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Trust the above solution helps.

Cheers,

Edward