SOLUTION: The marching band has more than 100 members but fewer than 200 members. When they line up in rows of 4 there is one extra person. When they line up in rows of 5 there are two extr

Algebra ->  Equations -> SOLUTION: The marching band has more than 100 members but fewer than 200 members. When they line up in rows of 4 there is one extra person. When they line up in rows of 5 there are two extr      Log On


   

Question 1049067: The marching band has more than 100 members but fewer than 200 members. When they line up in rows of 4 there is one extra person. When they line up in rows of 5 there are two extra people. When they line up in rows of 7 there are 3 extra people. How many members are in the marching band?

Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
n= number of members of the marching band.
If the band enrolled 3 more members,
they would have n%2B3 members.
Then, they could group there members in lines of 4, 5, or 7,
And they would have full, even lines.
That means that n%2B3 is a multiple of r, 5, and u.
The smallest such number is 4%D75%D77=140 ,
and the other such numbers are multiples of 140, all much greater than 20p.
So, n%2B3=140 ,and
the band has 140-3=highlight%28137%29 members.