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Home » \(b - 3 = -7 \Rightarrow b = -4\) - Feedz API

\(b - 3 = -7 \Rightarrow b = -4\) - Feedz API

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 Since 15 exceeds the limit, the largest valid multiple is 12.

📌 Therefore, the largest possible value of \( v \) is \(\boxed{12}\).

📌 How many positive 3-digit numbers are divisible by 9 and end with the digit 3?

📌 We seek 3-digit numbers divisible by 9 and ending in 3. A number divisible by 9 has its digit sum divisible by 9. Also, the number must end in 3, so let it be of the form \( 100a + 10b + 3 \), where \( a \in \{1,2,\dots,9\} \), \( b \in \{0,1,\dots,9\} \), and the number is divisible by 9.

📌 Let \( N = 100a + 10b + 3 \). We require \( N \equiv 0 \pmod{9} \). Since \( 100 \equiv 1 \pmod{9} \), \( 10 \equiv 1 \pmod{9} \), so:

📌 N \equiv a + b + 3 \pmod{9}

📌 a + b + 3 \equiv 0 \pmod{9} \quad \Rightarrow \quad a + b \equiv 6 \pmod{9}

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2x + 3y &= 16 \\
4x - y &= 9
Multiply the second equation by 3: \(12x - 3y = 27\).
Add to the first equation: \(2x + 3y + 12x - 3y = 16 + 27\).
Simplify: \(14x = 43\).
Solve for \(x\): \(x = 43 / 14\).
Substitute \(x\) into the first equation: \(2(43/14) + 3y = 16\).
Simplify: \(86/14 + 3y = 16\), or \(3y = 16 - 43/7\).
Convert: \(3y = 112/7 - 43/7 = 69/7\).
Solve for \(y\): \(y = 69 / 21 = 23/7\).

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