Question

When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation you can solve to get the answer.

Option 1

Daily fee $50

Cost per mile $0.15



Option 2

Daily fee $65

Unlimited miles

Answer 1

• variable; m (miles you must travel)
• equation: 65 < 50 +0.15m
• solution: m > 100

Explanation:

It is often convenient to choose a variable that has some mnemonic value with respect to what it represents. Here, we're asked for "miles you must travel", so the variable "m" seems appropriate for representing miles.

The fee for Option 1 is ...

50 + 0.15m

The fee for Option 2 is ...

65

For Option 2 to be the better option, its cost must be less than that for Option 1:

65 < 50 +0.15m . . . . . "equation" for getting the answer

To solve this equation, subtract 50 and divide by the coefficient of m.

(65 -50)/0.15 < m

100 < m

You must travel more than 100 miles for Option 2 to be better.