precal question

Question

It is estimated that the annual cost of driving a certain new car is given by the formula

C = 0.36m + 2900

where m represents the number of miles driven per year and C is the cost in dollars. Jane has purchased such a car and decides to budget between $7220 and $8660 for next year's driving costs. What is the corresponding range of miles that she can drive her new car? (Enter your answer using interval notation.)

 

Answer 1

Hello, Viviana,

In this problem, C represents the money spent on the car over one year. The 0.36 represents the cost per mile ($/mile) and the $2900 is fixed cost, regardless of miles driven (insurance, etc.)

We are told Jane can spend between $7270 and $8660 for the coming year. The number of miles can be calculated for each amount by entering each into the equation to calculate m, the number of miles. For the $7270:

$7270 = 0.36m + $2900

$7270 - $2900 = 0.36m (subtract 2900 from both sides)

$4320 - 0.36m

4320/0.36 = m

m = 12000 miles for the $2900

Do the same for the $8660 and m = 16000

Jane can drive between 12000 and 16000 miles for her budget range.