1. **Problem Statement:** Alex needs to rent a minivan for a week. Two companies offer different pricing schemes: - Easyvans charges a flat fee of 230 plus 0.10 per kilometer. - Cars for All Seasons charges a flat fee of 150 plus 0.26 per kilometer. We need to write equations for each company, graph them, and decide which is better for Alex. 2. **Define Variables and Write Equations:** Let $x$ be the number of kilometers driven. - Easyvans cost: $C_1 = 230 + 0.10x$ - Cars for All Seasons cost: $C_2 = 150 + 0.26x$ 3. **Graphing the Equations:** Both are linear equations with $x$ as the independent variable (kilometers) and $C$ as the dependent variable (cost). - Easyvans starts at 230 and increases by 0.10 per km. - Cars for All Seasons starts at 150 and increases by 0.26 per km. 4. **Find the Break-even Point:** To find when both costs are equal, solve: $$230 + 0.10x = 150 + 0.26x$$ Subtract 150 from both sides: $$230 - 150 + 0.10x = 0.26x$$ Simplify: $$80 + 0.10x = 0.26x$$ Subtract 0.10x from both sides: $$80 = 0.26x - 0.10x$$ $$80 = 0.16x$$ Divide both sides by 0.16: $$x = \frac{80}{0.16}$$ $$x = 500$$ 5. **Interpretation:** - For $x < 500$ km, Easyvans is more expensive because of the higher base fee. - For $x > 500$ km, Cars for All Seasons becomes more expensive due to the higher per km rate. 6. **Recommendation:** - If Alex plans to drive less than 500 km, Cars for All Seasons is cheaper. - If Alex plans to drive more than 500 km, Easyvans is cheaper. **Final answer:** - Equations: $C_1 = 230 + 0.10x$, $C_2 = 150 + 0.26x$ - Break-even at $x=500$ km - Choose Cars for All Seasons if driving less than 500 km, otherwise Easyvans.