Equations,money problems-help please

Question

Before hiring a car for a day trip, Kyle called several car hire services for some quotes.

Company:                         Cost Per day:

Sam’s Car Hire                  $25, plus $0.07 (7 cents) for each km.

Fleet Car Hire                    $50 for each day.

Daytripper’s Car Hire        $35, plus $0.05 (5 cents) for each km.

1. Set up a table of values for each car hire firm showing trips from 0km to 450km in 50km increments.

 

Let K stand for number of kilometres travelled

Let Cs stand for Sam’s hire cost

Let Cf stand for Fleet hire cost

Let Cd stand for Daytripper’s hire cost

 

a)      For each company write an equation for the cost.

b)      Plot three equations on the same graph.

Let the x axis have the distance with values from 0 to 600km, and the y axis show the cost

C with values from 0 to $80.

c)       Explain which deal is better for

(i)                  Short trips ?

(ii)                Long trips?

Sometimes it makes no difference which company you use.

d)      For what distances does:

(i)                  Cs=Cf?

(ii)                Cf=Cd?

(iii)               Cs=Cd

 

 

Answer 1

1) kyle called several car hire services

k	Cs	Cf	Cd
0	25	50	35
50	28.5	50	37.5
100	32	50	40
150	35.5	50	42.5
200	39	50	45
250	42.5	50	47.5
300	46	50	50
350	49.5	50	52.5
400	53	50	55
450	56.5	50	57.5

 

Answer 2

(1). Make the table :

k	Cs = 25 + 0.07k	Cf = 50	Cd = 35 + 0.05k
0	Cs = 25 + 0.07(0) = 0	50	Cd = 35 + 0.05(0) = 35
50	Cs = 25 + 0.07(50) = 28.5	50	Cd = 35 + 0.05(50) = 37.5
100	Cs = 25 + 0.07(100) = 32	50	Cd = 35 + 0.05(100) = 40
150	Cs = 25 + 0.07(150) = 35.5	50	Cd = 35 + 0.05(150) = 42.5
200	Cs = 25 + 0.07(200) = 39	50	Cd = 35 + 0.05(200) = 45
250	Cs = 25 + 0.07(250) = 42.5	50	Cd = 35 + 0.05(250) = 47.5
300	Cs = 25 + 0.07(300) = 46	50	Cd = 35 + 0.05(300) = 50
350	Cs = 25 + 0.07(350) = 49.5	50	Cd = 35 + 0.05(350) = 52.5
400	Cs = 25 + 0.07(400) = 53	50	Cd = 35 + 0.05(400) = 55
450	Cs = 25 + 0.07(450) = 56.5	50	Cd = 35 + 0.05(450) = 57.5

 

(a).

Company name                          Equation for the cost

Sam’s Car Hire                           C_s = 25 + 0.07k

Fleet Car Hire                             C_f = 50

Daytripper’s Car Hire                  C_d = 35 + 0.05k.

 

(b). Plot three equations on the same graph.

 

 

C).

(i). From the graph, Sam’s Car Hire company deals is better for Short trips.

(ii). From the graph, Fleet Car Hire company deals is better for Long trips.

 

(d).

(i). C_s = C_f

⇒ 25 + 0.07k = 50

⇒ 0.07k = 25

⇒ k = 357.143 km.

 

(ii). C_f = C_d

⇒ 50 = 35 + 0.05k

⇒ 15 = 0.05k

⇒ k = 300 km

 

(iii). C_s = C_d C_f = 50 C_d = 35 + 0.05k.

⇒ 25 + 0.07k = 35 + 0.05k

⇒ 0.02k = 10

⇒ k = 500 km.