Question

The difference between a two-digit number and that number reversed is 18. What could that number be? List all possibilities.

Answer 1

A two digit number can be written like AB or 10*A + B ( for example the number 36 can be written like 3*10 + 6 = 36)
You can write this problem as

10*A + B - (10*B + A) = 18
10*A + B - 10*B - A = 18
9*A - 9*B = 18
9(A - B) = 18
A - B = 2

A and B are digits, that means that both are either 0,1,2,3,4,5,6,7,8 or 9 (except that A cannot be 0 bcs the first digit in a two digit number cannot be 0)

So the combinations are

9 - 7 = 2
8 - 6 = 2
7 - 5 = 2
6 - 4 = 2
5 - 3 = 2
4 - 2 = 2
3 - 1 = 2
2 - 0 = 2

And we have the numbers:
97 ( B is 79)
86 ( B is 68)
75 ( B is 57)
64 ( B is 46)
53 ( B is 35)
42 ( B is 24)
31 ( B is 13)
20 ( B is 2)

Answer 2

There are two way to write two digit number i.e  $xy$ or $10\times x+y$.  The all possible number can be determine by system equation.

The all possible number could be 97 or 79, 86 or 68, 75 or 57, 64 or 46, 53 or 35, 42 or 24, 31 or 13, 20 or 2.

Given:

Difference between two digit number and that number reversed is 18.

Let the digit on 10th place is $x$.

Let the digit on one place is $y$.

The difference between a two digit number and that reversed is,

$10\times x + y - (10\times y + x)$

Write the system equation.

$\begin{aligned}\\10\times x + y - (10\times y + x)=18\\10x+y-10y-x=18\\9x-9y=18\\x-y=9\\\end$

The $x$ and $y$ both are the digit, so it could be $0,1,2,3,4,5,6,7,8,9$. The $x$ can not be $0$ because first digit cannot be zero.

Thus, the number combination are as follows.

$9 - 7 = 2\\8 - 6 = 2\\7 - 5 = 2\\6 - 4 = 2\\5 - 3 = 2\\4 - 2 = 2\\3 - 1 = 2\\2 - 0 = 2$

Hence, the all possible number could be 97 or 79, 86 or 68, 75 or 57, 64 or 46, 53 or 35, 42 or 24, 31 or 13, 20 or 2.

Learn more about Number here:

https://brainly.com/question/17211010