SOLUTION: ricky has some stickers in a box. if he puts the stickers into bags of 9. he will have no stickers left over. if he puts them into bags of 10, he will have 2 stickers left over. wh

 
Let N = number of stickers Ricky has in his box.

 
So N is a multiple of 9, so N=9P, for some positive integer P.

 
So N is 2 more than a multiple of 10, so N=9P=10Q+2, for some positive integer Q.

We write the larger coefficient (in absolute value), 10, in terms of the nearest
multiple of the smaller coefficient (in absolute value), 9. So we write 10 as
9+1

    9P=10Q+2
    9P=(9+1)Q+2
    9P=9Q+Q+2
 9P-9Q=Q+2
9(P-Q)=Q+2 
  P-Q=(Q+2)/9

The right side is positive and will be an integer if Q is 2 less
than a multiple of 9, so Q could be 7,16,25,...  Since N=9P, N
will be smallest when P is smallest, so we take P=7

If Q is 7 then 9P=10Q+2
               9P=10(7)+2
               9P=70+2
               9P=72
                P=8

Since N=9P, N=72

The smallest possible number of stickers in the box is 72.

Edwin