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Home » The ratio of the original volume to the scaled volume is: - American Beagle Club

The ratio of the original volume to the scaled volume is: - American Beagle Club

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 A solution contains 40% alcohol. How many liters of pure alcohol must be added to 10 liters of this solution to make a 60% alcohol solution?

📌 Initially, there are \( 0.4 \times 10 = 4 \) liters of alcohol.

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

📌 The new total volume is \( 10 + x \) liters, and the new alcohol content is \( 4 + x \) liters.

📌 The equation is \( \frac{4 + x}{10 + x} = 0.6 \).

📌 Solving, \( 4 + x = 0.6(10 + x) \) leads to \( 4 + x = 6 + 0.6x \).

📌 Simplifying, \( 0.4x = 2 \) gives \( x = 5 \).

📌 Check using the Pythagorean theorem: \( 7^2 + 24^2 = 49 + 576 = 625 \).

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