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?
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
.
