Number theory 17 people try dividing a box of sweets among t

Number theory:

17 people try dividing a box of sweets among themselves but find that there are 3 sweets left over. One person leaves and the remaining group try again to divide the number of sweets amongst themselves but find that there are now 10 sweets left over. Yet another person leaves, and the remaining people find that that number of sweets can be distributed evenly between them. What does this say about the number of sweets in the box?

Solution

Let every person is getting x sweets.

So in first case total sweets = 17x +3

in second case total sweets = 16x+10

and in third case, total sweets = 15x

so by first and second equation

17x+3= 16x+10

or 17x -16x = 10-3

or x= 7

so total sweets = 15 x = 15 x 7 = 105

so there are total 105 sweets in the box.

Answer