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Home » Divide by 3: \( x = \frac153 = 5 \). - Imagemakers

Divide by 3: \( x = \frac153 = 5 \). - Imagemakers

📅 May 1, 2026 👤 scraface

May 01, 2026

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🔥 Popular Posts

We seek 3-digit numbers divisible by 9 and ending in 3. A number divis...
Let \( N = 100a + 10b + 3 \). We require \( N \equiv 0 \pmod{9} \). Si...
N \equiv a + b + 3 \pmod{9}
We need:
a + b + 3 \equiv 0 \pmod{9} \quad \Rightarrow \quad a + b \equiv 6 \pm...
So \( a + b = 6 \) or \( a + b = 15 \) (since \( a \geq 1 \), \( b \le...
First, count solutions to \( a + b = 6 \), \( a \geq 1 \), \( b \geq 0...
\( a \) ranges from 1 to 6 → \( b = 6 - a \geq 0 \), so 6 solutions.
Now, \( a + b = 15 \):
\( a \geq 6 \) (since \( b \leq 9 \)), and \( a \leq 9 \). So \( a = 6...

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