Question

for every positive 2-digit number,x,with tens digit t and units digit u, let y be the 2-digit number formed by reserving the digits of x. which of the following expressions is equivalent to x-y
a. 9(t-u)
b. 9(u-t)
c. 9t-u
d. 9u-t
e. 0

Answer 1

some two digit number with t as the tens digit and u as the units digit
So this means,
x = 10t+u
Example: t = 5 and u = 3, so x = 10t+u = 10*5+3 = 53

In contrast,
y = 10u+t
because the tens and units digits have been swapped

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

Answer 2

Hey MATE!

According to the question,

x = 10 t + u (original number)

y = 10 u + t (new number by reversing the digits)

x - y ===>


10 t - u
- 10 u -t
----------------
9t - 9u


=) 9(t -u)


Hope it helps

Hakuna Matata :))