Question

The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven.

c = md + b

The cost is $4600 for 10 000 km and $9100 for 25 000 km.

(a) Determine the values of m and b.

(b) Write c as a function of d.​

Answer 1

Solution:

(a)

c = md + b

The cost is $ 4600 for 10 000 km

4600 = m (10 000) + b

10 000 m + b = 4600

b = -10 000 m + 4600 ------- (i)

The cost is $ 9100 for 25 000 km

9100 = m (25 000) + b

9100 = 25 000 m + b

25 000 m + b = 9100

b = -25 000 m + 9100 --------- (ii)

From equation (i) and (ii) we get;

-10 000 m + 4600 = -25 000 m + 9100

-10 000 m + 25 000 m = 9100 – 4600

15 000 m = 4500

m = 4500/15 000

m = 3/10

m = 0.3

Now, put the value of m = 0.3 in equation (i) we get;

b = -10 000 (0.3) + 4600

b = -3000 + 4600

b = 1600

Answer: m = 0.3 and b = 1600

(b) c = md + b

m = 0.3

b = 1600

c = 0.3d + 1600

Answer: c = 0.3d + 1600