SOLUTION: The sum of the digits of a two digit number is 10. If the digits are reversed, the number is increased by 72. What is the original number?

Question 568506: The sum of the digits of a two digit number is 10. If the digits are reversed, the number is increased by 72. What is the original number?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
Let u = the units digit of the original number
Let t = the tens digit
The number can be written as 10t + u
Given: Sum of the digits is 10. When the digits are reversed, the number is increased by 72.
t + u = 10 -> u = 10 - t
10u + t = 10t + u + 72
9u - 9t = 72
9(10-t) - 9t = 72
Solve for t:
90 - 18t = 72
18t = 18
t = 1
Therefore, u = 9
So the number is 19
Check:
91 = 19 + 72

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