# Equations,money problems-help please

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 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

asked Dec 22, 2013

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

answered Jan 29, 2014

(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                           Cs = 25 + 0.07k

Fleet Car Hire                             Cf = 50

Daytripper’s Car Hire                  Cd = 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). Cs = Cf

⇒ 25 + 0.07k = 50

⇒ 0.07k = 25

⇒ k = 357.143 km.

(ii). Cf = Cd

⇒ 50 = 35 + 0.05k

⇒ 15 = 0.05k

⇒ k = 300 km

(iii). Cs = Cd Cf = 50 Cd = 35 + 0.05k.

⇒ 25 + 0.07k = 35 + 0.05k

⇒ 0.02k = 10

⇒ k = 500 km.

answered Aug 21, 2014