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?

Let us assume the number of band members = x
Let assume the number of chorale members = y
Then
x = y + 30
(x + 10)/(y + 10) = 3/2
2(x + 10) = 3(y + 10)
2x + 20 = 3y + 30
2x - 3y = 10
Putting the value of x from the first equation in the second equation, we get
2x - 3y = 10
2(y + 30) - 3y = 10
2y + 60 - 3y = 10
y = 50
Putting y = 50 in the first equation we get
x = 50 + 30
   = 80
From the above deductions, we can easily conclude that the number of band members is 80. I hope that this is the answer that has actually come to your help.