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Home » This is a geometric sequence: a = 300, r = 1.15 - Silent Sales Machine

This is a geometric sequence: a = 300, r = 1.15 - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Let \( x \) be the liters of water added.

📌 New total volume = \( 50 + x \) liters.

📌 New water content = \( 30 + x \) liters.

📌 Set up the equation: \( \frac{30 + x}{50 + x} = 0.8 \).

📌 Solving, \( 30 + x = 0.8(50 + x) \) → \( 30 + x = 40 + 0.8x \) → \( 0.2x = 10 \) → \( x = 50 \) liters.

📌 If the sum of the squares of two consecutive integers is 85, what are the integers?

📌 Simplifying: \( x^2 + x^2 + 2x + 1 = 85 \) → \( 2x^2 + 2x - 84 = 0 \).

📌 Factoring: \( (x + 7)(x - 6) = 0 \).

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