The sum of the digits of a two-digit number is 16. if the digits are reversed, the new number is 18 less than the original number. find the original number.

Equation

Let one digit be x

Let the other digit = y

x + y = 16

Let the original number = 10x + y

Let the reverse number = 10y + x

10x + y - 18 = 10y + x

Comment

Bring the letters to the left and the number 18 to the right.

10x - x + y - 10y = 18 Combine like terms.

9x - 9y = 18 Divide both sides by 9

x - y = 2

Set up a set of equations and add.

x + y = 16

x - y = 2 Now add

2x = 18 Divide by 2

x = 18/2

x = 9

x + y = 16

9 + y = 16 Subtract 9 from both sides.

y = 16 - 9

y = 7

Check

Original number = 97

Reversed number 79

Difference 18 and it checks.