SOLUTION: the sum of the digits of a two-digit number is 12. if the digits are reversed, the new number is 18 less than the original number. find the original number.

Algebra ->  Systems-of-equations -> SOLUTION: the sum of the digits of a two-digit number is 12. if the digits are reversed, the new number is 18 less than the original number. find the original number.      Log On


   

Question 5021: the sum of the digits of a two-digit number is 12. if the digits are reversed, the new number is 18 less than the original number. find the original number.
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = tens digit
u = units digit
10t + u = value of the number
10u + t = value of the number with digits reversed

Two equations:
"Sum of the digits is 12."
t+u = 12 FIRST EQUATION

"If the digits are reversed, the new number is 18 less than the original number." OR "Reversed number = original number - 18"
10u + t = 10t + u - 18
9u - 9t = - 18

Divide by 9:
u - t = -2 SECOND EQUATION
u + t = 12 FIRST EQUATION

Add equations together:
2u = 10
u = 5

u+t = 12
5 + t = 12
t = 7

Original number = 75
Reverse digits = 57

Check: If you reverse the digits, the NEW NUMBER IS 18 less than ORIGINAL NUMBER. Observe, the new number IS 57 which is 18 less than 75. It checks!!!