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Home » We seek the smallest positive integer \( n \) such that: - Imagemakers

We seek the smallest positive integer \( n \) such that: - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 A chemist mixes a 20% acid solution with a 50% acid solution to obtain 30 liters of a 35% acid solution. How many liters of the 20% solution are used?

📌 Let \(x\) = liters of 20% solution, then \(30 - x\) = liters of 50% solution

📌 Total acid: \(0.20x + 0.50(30 - x) = 0.35 \times 30 = 10.5\)

📌 \(0.20x + 15 - 0.50x = 10.5 \Rightarrow -0.30x = -4.5 \Rightarrow x = 15\)

📌 #### 15 liters

📌 A train leaves Station A at 60 km/h. Two hours later, a faster train leaves Station A on the same line at 90 km/h. How long after the first train leaves will the second train catch up?

📌 First train head start: \(60 \times 2 = 120\) km

📌 Relative speed: \(90 - 60 = 30\) km/h

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