Question

If t and u are in the tens and ones digits of a

positive integer, n, and the number that results
after reversing the digits is 18 more than n,
which of the following provides t in terms of u.
A.
B.
C.
D.
E.
10-u
u-2
u-1
u+1
u +2

Answer 1

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.