Question 1139869
let the number of stickers in the box be equal to x.


when he puts 9 stickers into each bag, then the number of bags is equal to x / 9 with no stickers left over.


when he puts 10 stickers into each bag, then the number of bags is equal to x / 10 with 2 stickers left over.


since there are no left over stickers when you divide the number of stickers in the box by 9, then the number of stickers in the box has to be a multiple of 9.


that means that the numbers of stickers in the box can be equal to 9 or 18 or 27 or 36 or 45 or 54 or 63 or 72 or 81 or 90 or any other multiple of 9 going up to forever, if need be.


you want, however, to find the smallest number of stickers that can be in the box.


start from 9 stickers in the box and work your way up in multiples of 9 until you get a remainder of 2 when you divide the number of stickers by 10.


9 / 10 = 0 with a remainder of 9.
18 / 10 = 1 with a remainder of 8.
27 / 10 = 2 with a remainder of 7.
36 / 10 = 3 with a remainder of 6.
45 / 10 = 4 with a remainder of 5.
54 / 10 = 5 with a remainder of 4.
63 / 10 = 6 with a remainder of 3.
72 / 10 = 7 with a remainder of 2. ***** this is your solution.


the smallest number of stickers in the box has to be 72.


take 72 and divide it by 9 and you get 8 with no stickers left over.


take 72 and divide it by 10 and you get 7 with 2 stickers left over.


your solution is that the minimum number of stickers in the box has to be 72.