The sum of the digits of a two-digit number is 10, while when the digits are reserved, the number decreases by 54. Find the changed number.Options28192721
Question
The sum of the digits of a two-digit number is 10, while when the digits are reversed, the number decreases by 54. Find the changed number.
Options: 28, 19, 27, 21
Solution
Let's denote the tens digit as X and the units digit as Y.
From the problem, we know that:
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X + Y = 10 (The sum of the digits is 10)
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10Y + X = 10X + Y - 54 (When the digits are reversed, the number decreases by 54)
We can simplify the second equation to 9Y = 9X - 54, or Y = X - 6.
Substitute Y = X - 6 into the first equation, we get X + X - 6 = 10, or 2X = 16, so X = 8.
Substitute X = 8 into Y = X - 6, we get Y = 2.
So, the original number is 82, and the changed number is 28. Therefore, the answer is 28.
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