Question

Alamo car rental changes $45 a day to rent a mid-size vehicle plus six cents per mile. Hertz car

changes $30 a day plus ten cents per mile for the same car. How many miles would you need to drive for both
companies to charge the same price?

Answer 1

Let's write our formulas for both companies. I'll use the letter
`A` for Alamo and
`H` for Hertz.

• 
  `A=45+0.06(mile)`
• 
  `H=30+0.10(mile)`

In order for both companies to pay the same price, we need to equalize these two equations.

• 
  `A=H`
• 
  `45+0.06(mile)=30+0.10(mile)`
• 
  `45-30=0.10(mile)-0.06(mile)`
• 
  `15=0.04(mile)`
• 
  `(15)/(0.04) =mile`
• 
  `375=mile`

If we drive
`375` miles, we pay the same price to both companies.