Question 262678
x is the divisor
y is the result
r is the remainder


if the remainder is always 10, then the number of 100 - 10 = 90 must be divisible without a remainder.


our equation becomes:


90/x = y with no remainder.


multiply both sides of this equation by x to get:


90 = x*y


find all the factors of x and you will be able to find the anser.


90 equals:
1*90
2*45
3*30
6*15
9*10


now take these factors and divide them into 100.


100/1 = 100 with no remainder
100/90 = 1 with a remainder of 10
100/2 = 50 with no remainder
100/45 = 2 with a remainder of 10
100/3 = 33 with a remainder of 1
100/30 = 3 with a remainder of 10
100/6 = 16 with a remainder of 4
100/15 = 6 with a remainder of 10
100/9 = 11 with a remainder of 1
100/10 = 10 with a remainder of 0.


narrow it down to all those with a remainder of 10 and you get:


100/90
100/45
100/30
100/15


the divisor had to be greater than 10.


the smallest divisor is 15.


the largest divisor is 90.


your answer is:


the sum of the smallest and the largest divisor is 90 + 15 = 105.