Question

Every musician in the band plays either the flute or the drum (but not both). The ratio of flutists to drummers is 7 : 1. If 2 drummers join the group and 6 flutists quit, the ratio of flutists to drummers would be 3 : 1. How many musicians were in the original ensemble? 4. A sloth is swimming in the Charles River at 20 feet per minute. How fast is the sloth swimming in smoots per hour? One smoot is equal to 5 feet, 7 inches. Write your final answer as a simplified fraction.

Answer 1

the answer is 5!!!

Step-by-step explanation: hope this helps

Answer 2

Number of drummers in original ensemble
`=3`

Number of flutists in original ensemble
`=21`

Explanation:

The ratio of flutists to drummers is
`7:1`

Let number of flutists and drummers be
`7x` and
`x`.

As 2 drummers join the group and 6 flutists quit,

Number of drummers =
`x+2`

Number of flutists =
`7x-6`

New ratio of flutists to drummers =
`3:1`

So,

`(7x-6)/(x+2)=(3)/(1)\\ 7x-6=3(x+2)\\7x-6=3x+6\\7x-3x=6+6\\4x=12\\x=3`

So,

Number of drummers in original ensemble
`=x=3`

Number of flutists in original ensemble
`=7x=7(3)=21`