SOLUTION: When 100 is divided by some positive integer x, the remainder is 10. What is the sum of the smallest and largest values of x?
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Question 262678: When 100 is divided by some positive integer x, the remainder is 10. What is the sum of the smallest and largest values of x?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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.
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