SOLUTION: You are given the equation 3a + b = 200 where a and b are positive integers. Determine the number of solutions (a,b) for the given equation. HELP!!!!!!!!!!!!!!!!!

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: You are given the equation 3a + b = 200 where a and b are positive integers. Determine the number of solutions (a,b) for the given equation. HELP!!!!!!!!!!!!!!!!!      Log On


   

Question 433657: You are given the equation 3a + b = 200 where a and b are positive integers. Determine the number of solutions (a,b) for the given equation.
HELP!!!!!!!!!!!!!!!!!
Answer by psbhowmick(878) About Me  (Show Source):
You can put this solution on YOUR website!
3a+%2B+b+=+200
a+=+%28200+-+b%29%2F3

Since a has to be a positive integer then 200+-+b has to be a multiple of 3.
So 200-b can be 3, 6, 9,...., 198.

Thus 66 solutions are possible.

P.S.: a=b=0 cannot be a solution since both a and b has to be positive.