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Every musician in the band plays either the fife or the drum (but not both). The ratio of fifers to drummers is 7 : 1. If 2 drummers join the group and 6 fifers quit, the ratio of fifers to drummers would be 3 : 1. How many musicians were in the original ensemble?

 Aug 12, 2020
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Every musician in the band plays either the fife or the drum (but not both). The ratio of fifers to drummers is 7 : 1. If 2 drummers join the group and 6 fifers quit, the ratio of fifers to drummers would be 3 : 1. How many musicians were in the original ensemble?  

 

                                                                  F         7  

The ratio of fifers to drummers is 7 : 1.     ––   =   ––          Therefore, F  =  7D                                               (1)  

                                                                  D         1  

 

                                                          

If 2 drummers join the group               D + 2          1

                                                           –––––   =   ––           Therefore 3D + 6  =  F – 6   thus   F  =  3D + 12    (2)

and 6 fifers quit                                   F – 6          3

 

 

Substitute 3D + 12 for F in equation (1)         3D + 12  =  7D   

                                                                                12  =  4D

                                                                                  3  =  D                           3 Drummers   

 

Substitute 3 for D in equation (1)                               F  =  7 • 3

                                                                                   F  =  21                        21 Fifers  

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 Aug 12, 2020

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