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solomon's word for the wise - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 The area is \( x \times 2x = 10 \times 20 = 200 \) square meters.

📌 A solution contains 40% alcohol. If 10 liters of water is added to 30 liters of this solution, what is the new concentration of alcohol?

📌 initial alcohol content = 40% of 30 liters = 0.4 * 30 = 12 liters.

📌 Total volume after adding water = 30 liters + 10 liters = 40 liters.

📌 New concentration = \( \frac{12 \text{ liters}}{40 \text{ liters}} \times 100\% = 30\% \).

📌 A company’s profit, \( P \), is defined as revenue minus costs. If revenue is given by \( R = 50x \), costs are \( C = 30x + 100 \), and \( x \) is the number of units sold, express the profit function and find the profit when 20 units are sold.

📌 The profit function is \( P = R - C = 50x - (30x + 100) = 20x - 100 \).

📌 For \( x = 20 \), \( P = 20(20) - 100 = 400 - 100 = 300 \).

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