Question

A rental car company is running two specials. Customers can pay $50 to rent a compact car for the first day plus $6 for each additional day, or they can rent the same car for $40 the first day and $8 for every additional day beyond that. Camilla notices that, given the number of additional days she wants to rent the car for, the two specials are equivalent. How much would Camilla pay in total?

Answer 1

The number of additional days she wants to rent the car for the two specials are equivalent is 5 days.

Equation

Compact car:

• Fixed price = $50
• Additional price per day = $6

y = 50 + 6x

Another special:

• Fixed price = $40
• Additional price per day = $8

y = 40 + 8x

let

x = number of additional days

50 + 6x = 40 + 8x

• collect like terms

50 - 40 = 8x - 6x

10 = 2x

• Divide both sides by 2

x = 10/2

x = 5 days

Therefore, the number of additional days she wants to rent the car for, the two specials are equivalent is 5 days.

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