The sum of the digits of a two-digit number is 9. If 27 is addedto it, the digits of the number get reversed. The number is
Question
The sum of the digits of a two-digit number is 9. If 27 is added to it, the digits of the number get reversed. The number is
Solution
Let's solve this step by step:
Step 1: Let's denote the tens digit as "x" and the units digit as "y". So, the two-digit number can be written as 10x + y.
Step 2: According to the problem, the sum of the digits is 9. So, we have the equation x + y = 9.
Step 3: It's also given that if 27 is added to the number, the digits get reversed. So, the number becomes 10y + x. Therefore, we have the equation 10x + y + 27 = 10y + x.
Step 4: Simplify the equation from step 3 to get 9x - 9y = -27.
Step 5: Divide the entire equation by 9 to get x - y = -3.
Step 6: Now we have a system of two equations: x + y = 9 and x - y = -3. Solve this system to get x = 3 and y = 6.
So, the two-digit number is 36.
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