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Home » We want the smallest integer \(t\) such that: - American Beagle Club

We want the smallest integer \(t\) such that: - American Beagle Club

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 - 6b + 25b = 155 \Rightarrow 19b = 69 \Rightarrow b = \frac{69}{19}

📌 This is exact. So one bead costs $ \frac{69}{19} $ gold coins. But let's double-check the original equations with integer values.

📌 Try solving again using elimination:

📌 Multiply first equation by 5: $ 25t + 15b = 215 $

📌 Multiply second by 3: $ 6t + 15b = 93 $

📌 Then plug into $ 5t + 3b = 43 $:

📌 \cdot \frac{122}{19} + 3b = 43 \Rightarrow \frac{610}{19} + 3b = 43 \Rightarrow 3b = 43 - \frac{610}{19} = \frac{817 - 610}{19} = \frac{207}{19}

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