Mr. Hancock, the owner of two car dealerships in Newport, is holding a contest to see which one can sell the most cars. Newport Cars has already sold 5 cars, and Hancock's Autos has sold 15 cars. Going forward, the salespeople at Newport Cars think they can sell 3 cars per day, whereas the salespeople at Hancock's Autos are aiming for sales of 2 cars per day. If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied. How many cars will each lot have sold? Write a system of equations, graph them, and type the solution. ____ cars

Question

Mr. Hancock, the owner of two car dealerships in Newport, is holding a contest to see which one can sell the most cars. Newport Cars has already sold 5 cars, and Hancock's Autos has sold 15 cars. Going forward, the salespeople at Newport Cars think they can sell 3 cars per day, whereas the salespeople at Hancock's Autos are aiming for sales of 2 cars per day. If the salespeople's predictions are accurate, it won't be long before the two dealerships are tied. How many cars will each lot have sold?  Write a system of equations, graph them, and type the solution.  ____ cars

Bytelearn · Accepted Answer

Define Variables:  Let's define the variables: Let $ x $ be the number of days after the current sales. Newport Cars' total sales will be $ 5 + 3x $ (since they start with 5 cars and sell 3 per day). Hancock's Autos' total sales will be $ 15 + 2x $ (starting with 15 cars and selling 2 per day). Set Up Equation:  Set up the equation to find when both dealerships have sold the same number of cars: $ 5 + 3x = 15 + 2x $. Solve for x:  Solve for $ x $: Subtract $ 2x $ from both sides to get $ 3x - 2x = 15 - 5 $, which simplifies to $ x = 10 $.

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