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Home » 4a + 2b + c &= 11, \\ - Portal da AcÃºstica

4a + 2b + c &= 11, \\ - Portal da AcÃºstica

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \Rightarrow b = \frac{69}{19}

📌 Thus, one bead costs $ \boxed{\frac{69}{19}} $ gold coins.

📌 Question: A soil scientist measures the nutrient content in five soil samples taken at increasing depths, which form an arithmetic sequence. If the average nutrient level across the samples is 22 units, and the difference between the highest and lowest nutrient levels is 16 units, what is the nutrient level at the third sample?

📌 Solution: Let the five terms of the arithmetic sequence be $ a - 2d, a - d, a, a + d, a + 2d $.

📌 The average is 22, so:

📌 \frac{(a - 2d) + (a - d) + a + (a + d) + (a + 2d)}{5} = a = 22

📌 The total difference between highest and lowest is:

📌 The third sample has nutrient level $ a = 22 $.

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