If Claudia has a budget of $130 which company should he choose in order to travel the further distance?

Question

Claudia wants to rent a car for her trip. She calls two car rental companies to find out their rental rates for a particular vehicle. Mr.wheels rentals charges a flat rate of $90 plus $0.10 per mile traveled. Grand auto rentals charges a flat rate of $75 plus $0.15 per mile traveled. If Claudia plans to drive only 100 miles which company should she choose? For what driving distance would Claudia pay the same amount for both companies? 

Answer 1

Charge with Mr.Wheel (W) = 90 + .10 x D

Charges with Mr.Grand (G) = 75 + .15 x D

Where D is distance traveled.

 

i. D = 100

W = 90 + .10 x 100 = $100

G = 75 + .15 x 100 = $90

Claudia should go with Mr. Grand

 

ii 

90 + .10 x D = 75 + .15 x D

15 = .05 x D

D = 15/.05 = 300 miles

For 300miles, both company will charge same.

For D< 300, Mr. Grand would charge less and for D>300 Mr. Wheel will charge less.

 

Answer 2

For this problem, you need to write two linear equations that represent the cost for each rental company. The flat rate corresponds to the y-intercept while the cost per mile is equal to the slope. So you will use the slope-intercept form to write the equations. The slope-intercept form of a linear equation is y=mx+b where m is equal to the slope and b is equal to the y-intercept. The equations follow.

 

Mr. Wheels- y=.10x+90

Grand auto- y=.15x+75

 

Now, plug 100 into each equation to calculate the cost of traveling 100 miles. 

 

Mr. Wheels- y=.10(100)+ 90=10+90=100

Grand auto- y=.15(100)+75+15+75=90

 

Therefore, Grand auto is the best choice if you are traveling 100 miles as it offers the lower price. 

 

To calculate where the prices are the same, you need to solve the system of equations (simultaneous equations). You can use substitution or elimination. I will use substitution and substitute the y of the Grand auto equation into the y of the Mr. Wheels equation and solve for x.

 

.15x+75=.10x+90

.05x=15

x=300

 

So at 300 miles, the cost will be the same for each company. The cost will be $120 for both companies.