Question

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 Ronald's Rentals, customers will pay $44 to rent a mid-sized car for the first day, plus $6 for each additional day. At Morristown Rent-a-Car, the price for a mid-sized car is $42 for the first day and $8 for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How many additional days would that take? How much would the customer pay?For additional days, the customer would pay $ either way.

Answer 1

We will have one equation for each company.

Let the total cost be y and the number of additional days be x.

Then, for Roland's Rentals, we will have a total cost of 44 plus 6 times the nunmber of additional days, that is:

`y=44+6x`

And for Morristown Rent-a-Car we will have a totl cost of 42 plus 8 times the number of additional days, that is:

`y=42+8x`

So, the system of equations is:

`\begin{gathered} y=44+6x \\ y=42+8x \end{gathered}`

Finding the solution is the same as finding the number of additional days, x, will give the same cost, y, for both.

To solve, we can substitute the first equation into the second:

`\begin{gathered} 44+6x=42+8x \\ 44-42=8x-6x \\ 2=2x \\ 2x=2 \\ x=1 \end{gathered}`

And now, we can input this solution into either equation to find the cost:

`\begin{gathered} y=44+6\cdot1 \\ y=44+6 \\ y=50 \end{gathered}`

Thus, for 1 additional day, the customer would pay $50 either way.