A rental car company is running two specials. Customers can pay $40 to rent a compact car for the first day plus $6 for each additional day, or they can rent the same car for $30 the first day and $7 for every additional day beyond that. Pamela notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How many additional days does Pamela want? Write a system of equations,

Answer: she wants to rent the car for 11 days.

Step-by-step explanation:

Let x represent the number of additional days that Pamela wants to rent the car for.

Customers can pay $40 to rent a compact car for the first day plus $6 for each additional day. This means that the total cost of using this special for x days would be

40 + 6 (x - 1) = 40 + 6x - 6

= 34 + 6x

Also, they can rent the same car for $30 the first day and $7 for every additional day beyond that. This means that the total cost of using this special for x days would be

30 + 7 (x - 1) = 30 + 7x - 7

= 23 + 7x

Since she found out that the two specials are equivalent for x days, then

34 + 6x = 23 + 7x

7x - 6x = 34 - 23

x = 11