Question

Hodel just got her driver's license. Her parents offer her two options. 1. They'll buy her a used car that will cost her $0.50 per mile in gas and maintenance fees. 2. They'll buy her a new hybrid car but she'll have to contribute $5,000 to the cost. The new car will then cost her an additional $0.10 per mile in gas and maintenance fees. If she plans to keep the car until she graduates from college in six years and she intends to drive it 10,000 miles each year, which option will cost her less?

Answer 1

The second option will cost her less than the first one.

Explanation:

In order to solve this problem we will create two functions to represent the cost of the car in function of the miles drove by her.

For the first option we have:

`cost_1(x) = 0.5*x`

For the second option we have:

`cost_2(x) = 5000 + 0.1*x`

Since she intends to drive it for 10,000 miles per year for 6 years, then the total mileage she intends to drive her car is 60,000 miles. Applying this to the formula of each car and we have:

`cost_1(60000) = 0.5*60000 = 30000`

`cost_2(60000) = 5000 + 60000*0.1 = 11000`

The second option will cost her less than the first one.