To determine the relationship between the tens digit (t) and the ones digit (u) in a positive integer n, we need to analyze the given information.
The number that results from reversing the digits of n is 18 more than n. Let's express this relationship mathematically:
10u + t = n (1)
10t + u = n + 18 (2)
We can solve this system of equations to find the relationship between t and u.
First, let's simplify equation (2) by subtracting 18 from both sides:
10t + u - 18 = n
Next, let's substitute n from equation (1) into equation (2):
10t + u - 18 = 10u + t
Now, let's rearrange the equation:
10t - t - 10u + u = 18
Combining like terms:
9t - 9u = 18
Divide both sides of the equation by 9:
t - u = 2
Therefore, the correct answer is option E: t = u + 2.