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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two rental car companies are running specials this month. At Kate's Rentals, customers will pay to rent a mid-sized car for the first day, plus for each additional day. At Fairfax Rent-a-Car, the price for a mid-sized car is for the first day and for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How much would the customer pay? How many additional days would that take?The customer would pay _____ either way for _____ additional days.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Two rental car companies are running specials this month. At Kate's Rentals, customers will pay to rent a mid-sized car for the first day, plus for each additional day. At Fairfax Rent-a-Car, the price for a mid-sized car is for the first day and for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How much would the customer pay? How many additional days would that take?The customer would pay _____ either way for _____ additional days.
- Set up equations: Let's set up the equations for both rental companies. For Kate's Rentals, the total cost after additional days is . For Fairfax Rent-a-Car, the total cost after additional days is .
- Find equal costs: Now, we need to find when the costs are the same, so we set the equations equal to each other: .
- Solve for d: Solve for by subtracting from both sides: . Then subtract from both sides: .
- Calculate d: Divide both sides by to find : .
- Find total cost: Substitute back into one of the original equations to find the total cost. Using Kate's Rentals equation: .
