**Math Puzzle: The Mysterious Number**
I am thinking of a three-digit number. The tens digit is five less than the hundreds digit, and the units digit is eight more than the tens digit. What is the number?
**Answer:** Let's denote the hundreds digit as \(H\), the tens digit as \(T\), and the units digit as \(U\). According to the given information:
1. \(T = H - 5\)
2. \(U = T + 8\)
Now, since we're dealing with three-digit numbers, the hundreds digit (\(H\)) must be greater than 0.
Let's solve the system of equations:
From equation (1):
\[T = H - 5\]
Substitute \(T\) in equation (2):
\[U = (H - 5) + 8\]
Combine like terms:
\[U = H + 3\]
Now, since \(U\) is a digit, it must be less than 10. Therefore:
\[0 \leq H + 3 < 10\]
Solving for \(H\):
\[0 \leq H < 7\]
Since \(H\) must be a positive digit, the only valid value is \(H = 6\).
Now, substitute \(H = 6\) back into the equations:
\[T = 6 - 5 = 1\]
\[U = 6 + 3 = 9\]
So, the mysterious number is \(619\).
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