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Home » \[ 2(3w) = 36 \] - Baxtercollege

\[ 2(3w) = 36 \] - Baxtercollege

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 Question: An organic chemist synthesizes a compound with molecular formula $ C_nH_{2n} $, where the ratio of carbon to hydrogen atoms satisfies $ \frac{a}{b} = 3 $ and their sum is $ a + b = 16 $. Find the value of $ a^2 - b^2 $.

📌 Solution: Given $ \frac{a}{b} = 3 $, let $ a = 3b $. Substituting into $ a + b = 16 $: $ 3b + b = 16 $, so $ b = 4 $ and $ a = 12 $. Now, $ a^2 - b^2 $ factors as $ (a - b)(a + b) = (12 - 4)(16) = 8 \times 16 = 128 $. Therefore, the value is $ \boxed{128} $.

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