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Home » Step 2: Compute midpoint and slope of side $AC$ - Blask

Step 2: Compute midpoint and slope of side $AC$ - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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

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

📌 A tank is filled by two pipes. Pipe A fills it in 5 hours, and Pipe B fills it in 3 hours. How long will it take to fill the tank if both pipes are used together?

📌 Pipe A's rate = \( \frac{1}{5} \) tank/hour, Pipe B's rate = \( \frac{1}{3} \) tank/hour.

📌 Combined rate = \( \frac{1}{5} + \frac{1}{3} = \frac{3}{15} + \frac{5}{15} = \frac{8}{15} \) tank/hour.

📌 Time to fill the tank = \( \frac{1}{\frac{8}{15}} = \frac{15}{8} \) hours = 1.875 hours.

📌 A mixture contains 60% water and 40% juice. How much water must be added to 50 liters of this mixture to achieve a new mixture that is 80% water?

📌 Initial water = 60% of 50 liters = 30 liters.

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