For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number...?

Question

formed by reversing the digits of x. Which of the following expressions is equivalent to x-y? (the answer is 9(t-u)..now how in the world do you do that?)

Answer 1

x=10t+u (t is tens digit & u is units digit)
y=10u+t (digits reversed)

x-y=10t+u - (10u+t)
=10t+u-10u-t
=9t-9u
=9(t-u)

Answer 2

x = 10t + u
y = 10u + t

x-y = 10t + u - (10u + t) = 9t - 9u = 9(t - u)

try it with a real number:

if x=48, then t=4 and u=8 and y=84;
thus: x-y = 48-84 = -36
9(t-u) = 9(4-8) = 9(-4) = -36

Answer 3

x = 10t + u the original number
y = 10u + t the number made by reversing the digits
The question is: what is x-y? Just do it...
x-y = (10t+u) - (10u+t) = 9t-9u = 9(t-u)
and you are home in time for ice cream

Answer 4

Number x is equal to 10t + u

Number y is equal to 10u + t

Difference (x - y) is (10t + u) - ( 10u + t) = 9t - 9u = 9(t - u)

Answer 5

x = 10t+u
y= 10u-t
x-y = 9t-9u = 9(t-u)