Question

the seventh and eighth grade bands held a joint concert. together there was 188 band members. if the eight grade band is 3 times as big as the seventh grade band, how big is the eight grade

Answer 1

Let the size of the seventh grade band be s
That means the size of the eighth grade band must be 3s because it is 3 times as big as the seventh grade band.
Combined, the two bands have 188 members.
3s and s combined is 4s. Thus 4s must equal 188.

4s = 188
s= 47
3s = 141

The eighth grade band has 141 members.

Answer 2

8th grade = 3x = 3(47) = 141 band members.

7th + 8th = 188

7th = x
8th = 3x

x + 3x = 188 ; x = 47 ; 47 + 3(47) = 47 + 141 = 188
4x = 188
4x / 4 = 188 / 4
x = 47 --> 7th grade

8th grade = 3x = 3(47) = 141

To check:
x + 3x = 188 ; x = 47 ;
47 + 3(47) = 188
47 + 141 = 188
188 = 188