Problem No. 26. Kate and her candies

A good packing plan is difficult to make.

Kate has some number of candies. If she puts the same number of candies in each of her 7 bags, two candies will be left. If she adds one more bag and still try to put the same number of candies in each bag, seven candies will be left. We know that Kate has less then 30 candies. How many candies does Kate have?

Parent tip

Since the total number of candies is less then 30, you can try to solve a problem with real candies. Try to divide the candies in equal sized groups according to the problem's conditions.

Solution

Kate has less than 30 candies, and if she puts the same number of candies in each of her 7 bags, two candies will be left, so she can have 2, 9, 16 or 23 candies (each of these numbers has the reminder equal to 2 when dividing with 7). If she try to put the same number of candies in each of 8 bags (one more bag than 7 bags), 7 candies will be left, and it is possible, only if she has 23 candies (because the number 23 is the number that has reminder equal to 7 when dividing with 8).