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.
