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?
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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?
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.
