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# pls help

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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

#1
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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