SOLUTION: The number n is a two digit number. When n is divided by 10 the remainder is 9, when n is divided by 9 the remainder is 8. What is the value of n?

Question 603906: The number n is a two digit number. When n is divided by 10 the remainder is 9, when n is divided by 9 the remainder is 8. What is the value of n?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The number n is a two digit number.
When n is divided by 10 the remainder is 9, when n is divided by 9 the remainder is 8.
What is the value of n?
:
has remainder of 9, Second digit has to be 9
19, 29, 39, 49, 59, 69, 79, 89, 99
:
has remainder of 8
26, 35, 44, 53, 62, 71, 80, 89, 98
:
n = 89
This is the brute force method, here is a formula, not quite sure why it works
= = 1
multiply by 90 to clear the denominators
10(n-8) - 9(n-9) = 1
10n - 80 - 9n + 81 = 90
n + 1 = 90
n = 90- 1
n = 89
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