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Home » \(x_1 = \frac124 = 3\) - Get link 4share

\(x_1 = \frac124 = 3\) - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Question: An entrepreneur develops a sustainable agriculture tool, selling 4 AI-powered sensors and 7 soil moisture meters for $315. A second purchase includes 2 sensors and 5 meters for $185. How much does a sensor cost in cents?

📌 Solution: Let $ s $ be the sensor price and $ m $ the meter price. The system is:

📌 4s + 7m = 315 \

📌 2s + 5m = 185

📌 Multiply the second equation by 2: $ 4s + 10m = 370 $. Subtract the first equation: $ 3m = 55 \Rightarrow m = rac{55}{3} $. Substitute back: $ 2s + 5 \cdot rac{55}{3} = 185 \Rightarrow 2s = 185 - rac{275}{3} = rac{280}{3} \Rightarrow s = rac{140}{3} pprox 46.67 $. Convert to cents: $ 4667 $ cents.

📌 oxed{4667}

📌 Question: An ichthyologist tracks two fish species' population trends with lines $ y = -3x + 18 $ (species A) and $ y = 4x - 2 $ (species B). Find their intersection point.

📌 Solution: Set $ -3x + 18 = 4x - 2 $. Solve: $ 18 + 2 = 7x \Rightarrow x = rac{20}{7} $. Substitute into $ y = -3 \cdot rac{20}{7} + 18 = -rac{60}{7} + rac{126}{7} = rac{66}{7} $. Intersection at $ \left( rac{20}{7}, rac{66}{7}

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