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Home » Can we place 4 non-adjacent H’s in 7 positions? - Londonproperty

Can we place 4 non-adjacent H’s in 7 positions? - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 Solution: Let $ x $ be the cost of an app icon in dollars and $ y $ the cost of a color theme. The system of equations is:

📌 4x + 6y = 32.40 \\

📌 3x + 2y = 18.30

📌 Multiply the second equation by 3: $ 9x + 6y = 54.90 $. Subtract the first equation: $ (9x + 6y) - (4x + 6y) = 54.90 - 32.40 $, yielding $ 5x = 22.50 $. Thus, $ x = 4.50 $ dollars, or $ \boxed{450} $ cents.

📌 Question: An archaeologist discovers 5 pottery shards and 2 stone tools worth \$48.50, and 3 pottery shards and 4 stone tools worth \$51.00. What is the value of one stone tool in dollars?

📌 Solution: Let $ p $ be the price of a pottery shard and $ s $ the price of a stone tool. The system is:

📌 5p + 2s = 48.50 \\

📌 3p + 4s = 51.00

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