SOLUTION: If 45 is added to a two-digit number, the result is a number with the same digits, but in reverse order. The sum of the digits is 11. What is the original number?

Question 377809: If 45 is added to a two-digit number, the result is a number with the same digits, but in reverse order. The sum of the digits is 11. What is the original number?

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assume the original number is 10a+b where a,b are digits. Since the order of the digits is reversed upon adding 45, we have
10a + b + 45 = 10b + a
9a - 9b = -45
a - b = -5
We are also given a + b = 11. Adding the last two equations together we have 2a = 6 --> a = 3. From this we can plug into either of the last two equations to obtain b = 8. Therefore the original number is 38.
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