Question

The band has 30 more members than the school chorale. If each group had 10 more members, the ratio of their membership would be 3:2. How many members are in the band? a. 50 members c. 80 members b. 45 members d. 32 members

Answer 1

80 members

Explanation:

Let the band members be= b and the chorale members= c

Then, according to question, b=c+30 and
`(b+10)/(c+10)=(3)/(2)`

⇒
`2(b+10)=3(c+10)`

⇒
`2b+20=3c+30`

⇒
`2b-3c=30-20`

⇒
`2b-3c=10`

Now, substituting the value of b=c+30, we get

⇒
`2(c+30)-3c=10`

⇒
`2c+60-3c=10`

⇒
`-c=-50`

⇒
`c=50`

Therefore,
`b=c+30`

`b=50+30=80`

Therefore, there are 80 members in the band.