GED Math: Solving Linear Inequality Word Problems with Rental Car Costs

Setting Up the Linear Inequality

• 🎯 The problem involves a car rental company charging $29 per day plus $0.15 per mile.
• 📅 Karen needs to rent a car for 2 weeks (14 days) and has a budget of $800.
• ✍️ The inequality is set up as: (Daily Cost * Number of Days) + (Cost per Mile * Number of Miles) ≤ Budget
• ➡️ This translates to: 29 * 14 + 0.15 * m ≤ 800, where 'm' represents the number of miles.

Solving for Maximum Miles

• 💰 First, calculate the fixed cost for 14 days: 29 * 14 = $406.
• ⚖️ Subtract this fixed cost from the total budget: $800 - $406 = $394.
• 📈 This leaves $394 to cover the mileage cost, so 0.15 * m ≤ 394.
• ➗ To find the maximum miles, divide the remaining budget by the cost per mile: m ≤ 394 / 0.15.

Determining the Final Answer

• 🧮 The calculation results in m ≤ 2,626.66....
• 📉 Since Karen cannot exceed her budget, the number of miles must be rounded down to the nearest whole number.
• ✅ The maximum number of miles Karen can drive without exceeding her $800 budget is 2,626 miles.