SOLUTION: a, b ,c are positive integers such that 10 > a > b > c > 0 N is the largest three digit number that has the digits a, b and c. K is the smallest three digit number that has the

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson  -> Lesson -> SOLUTION: a, b ,c are positive integers such that 10 > a > b > c > 0 N is the largest three digit number that has the digits a, b and c. K is the smallest three digit number that has the       Log On


   

Question 1078876: a, b ,c are positive integers such that 10 > a > b > c > 0
N is the largest three digit number that has the digits a, b and c.
K is the smallest three digit number that has the digits a, b and c.
Use algebra to show that the difference between N and K is always a multiple of 99.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

N = 100a+10b+c
K = 100c+10b+c

N-K = (100a+10b+c)-(100c+10b+a) = 100a+10b+c-100c-10b-a = 99a-99c = 99(a-c)

which is a multiple of 99 and it's positive since a > c

Edwin