Solutions to Linear Diophantine equation $15x+21y=261$ Question 

How many positive solutions are there to $15x+21y=261$?

What I got so far
$\gcd(15,21) = 3$ and $3|261$
So we can divide through by the gcd and get:
$5x+7y=87$
And I'm not really sure where to go from this point. In particular, I need to know how to tell how many solutions there are.

Hint $\ $ It's easy. $\rm\:x\ge 1\:\Rightarrow\: y = (87-5x)/7 \le \lfloor 82/7\rfloor = 11.\:$ Each of the intervals $[1,5], [6,10]$ contains precisely one solution for $\rm\:y,\:$ so it remains to check if $\rm\:y=11\:$ yields a solution.
Note that the (extended) Euclidean algorithm is not required, and this method works generally.
