Members of the west high school band were hard at work practicing for the annual homecoming parade.First they tried marching in rows of 12 but andrew was left by himself to bring up the rear. Then the director told the band to members to march in columns of eight but andrew was still left to march alone. Even when the band marched in rows of three Andrew was left out. Finally in exasperation,andrew told the band director that they should march in rows of five in order to have all the rows filled. He was right. Given that there were at least 45 musicians on the field but fewer than 200musicians how many students were there in the west high school band.

Answer 1

Which of these multiples of 8 plus 1 is also divisible by 5?

49, 57, 65, 73, 81, 89, 96

Is it also a multiple of 3 plus 1?

Answer 2

So the number has to be a multiple of 5 , between 45 and 200
when divided by 8 there is a remainder of 1
so it could be
49 57 65 73 81 89 97 105... 145 .... 185

when divided by 12 , there is a remainder of 1
so it could be
49 61 73 85 97 109 121 133 145 ... 205

the common number is all 3 restrictions is 145
So there were 145 students.

check:
1. 145 divides evenly be 5
2. 145/8 = 18 with remainder of 1
3. 145/12 = 12 with a remainder of 1