Question

PLEASE HELP I NEED THIS NOWWWThe 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

Answer:

$\large\boxed{31,\ 42,\ 53,\ 64,\ 75,\ 86,\ 97}$

Step-by-step explanation:

$a-\text{the digit of tens}\\b-\text{the digit of ones}\\\\10a+b-\text{the number}\\10b+a-\text{the number reversed}\\\\\bold{EQUATION:}\\\\(10a+b)-(10b+a)=18\\\\10a+b-10b-a=18\qquad\text{combine like terms}\\\\(10a-a)+(b-10b)=18\\\\9a-9b=18\qquad\text{divide both sides by 9}\\\\\dfrac{9a}{9}-\dfrac{9b}{9}=\dfrac{18}{9}\\\\a-b=2\to b=a-2\\\\\text{List of all solutions}\\\\a=3,\ b=3-2=1\\a=4,\ b=4-2=2\\a=5,\ b=5-2=3\\a=6,\ b=6-2=4\\a=7,\ b=7-2=5\\a=8,\ b=8-2=6\\a=9,\ b=9-2=7$