belle and her friends are planning a weekend trip to isle of palms, south carolina! they can rent either a…

belle and her friends are planning a weekend trip to isle of palms, south carolina! they can rent either a sedan or a fuel - efficient suv for the trip. the sedan will cost $180 to rent, while the suv will cost $200. belle estimates that the sedan will cost $0.11 per mile in fuel, while the suv will cost about $0.06 per mile. how many miles would belle and her friends need to drive for the total cost of the vehicles to be the same? simplify any fractions. miles

belle and her friends are planning a weekend trip to isle of palms, south carolina! they can rent either a sedan or a fuel - efficient suv for the trip. the sedan will cost $180 to rent, while the suv will cost $200. belle estimates that the sedan will cost $0.11 per mile in fuel, while the suv will cost about $0.06 per mile. how many miles would belle and her friends need to drive for the total cost of the vehicles to be the same? simplify any fractions. miles

Answer

Answer:

(400)

Explanation:

Step1: Set up cost equations

Let (x) be the number of miles. The total cost of the sedan (C_{s}=180 + 0.11x). The total cost of the SUV (C_{u}=200+0.06x).

Step2: Set the costs equal

Set (C_{s}=C_{u}), so (180 + 0.11x=200+0.06x).

Step3: Solve for (x)

Subtract (0.06x) from both sides: (180+0.11x - 0.06x=200+0.06x-0.06x), which gives (180 + 0.05x=200). Subtract (180) from both sides: (0.05x=200 - 180), so (0.05x=20). Divide both sides by (0.05): (x=\frac{20}{0.05}=400).