# A rental company charges $40.00 a day...Solve equations.

A rental company charges $40.00 a day plus $0.34 per mile to rent a moving truck. The total cost, y, for a day's rental if x miles are driven is described by y = 0.34x + 40. A second company charges $32.00 a day plus $0.44 per mile, so the daily cost, y, if x miles are driven is described by y = 0.44x + 32. The graphs of the two equations are shown in the same rectangular coordinate system.

a. Determine from the graph the x-coordinate of the intersection point of the two graphs.

Describe what this x-coordinate means in practical terms. Choose the correct answer below.

A. Both companies charge the same for 80 miles driven.

B. Both companies charge the $80 for the same number of miles driven.

C. The maximum amount of miles that can be driven is 80.

D. The maximum amount that both companies charge is $80.

b. Substitute the x-coordinate of the intersection point from part a into one of the two equations.

Find the corresponding value for y.

y = ?

Describe what this value represents in practical terms. Choose the correct answer below.

A. Both companies charge $67.20 for 80 miles driven.

B. Both companies always charge more than $67.20.

C. Both companies alyways charge less than $67.20.

D. Both companies charge $67.20 for 67 miles driven.

https://brainmass.com/math/graphs-and-functions/rental-company-charges-day-solve-equations-483670

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Please find below the solution.

(A)We have two equations

y=0.34x+40 and

y=0.44x+32

where x is the miles driven and y is the total cost for a day's rental

0.34x + 40 = 0.44x + 32

0.34x - 0.44x = 32-40

-0.10x = -8

0.10x=8

x= 8/0.10

x=80

now subsitute the value of x in first equation to get the value of y

y=0.34(80) + 40

y = 27.2 + 40

y = 67.2

So, (x,y) = (80,67.2) is the point of intersection

Both companies charge the same for 80 miles driven.

Option A is correct

(B) Subsitute the value of x in first equation to get the value of y

y=0.34(80) + 40

y = 27.2 + 40

y = 67.2

Both the companies charge $67.20 for 80 miles driven

Option A is correct.

Â© BrainMass Inc. brainmass.com October 4, 2022, 3:49 pm ad1c9bdddf>https://brainmass.com/math/graphs-and-functions/rental-company-charges-day-solve-equations-483670