mabel is comparing the prices of two car rental companies. company a charges $35 per day and an additional $15 as service charges. company b charges $42 per day and an additional $10 as service charges.

part a: write an equation to represent each company's total charges for renting a car for a certain number of days. for both equations (one for company a and one for company b), define the variable used. (4 points)

part b: which company would charge less for renting a car for 6 days? justify your answer. (3 points)

part c: how much money is saved by using the services of company a instead of company b to rent a car for 10 days? (3 points)

P = total Price

X = number of days

 Part A

Company A : P=35x+15

Company B: P=42X+10

Part B

X=6

Company A : 35(6) +15 = 225

Company B: 42(6)+10 = 262

 so Company A is cheaper

Part C

 x = 10

Company A: 35(10)+15 = 365

Company B: 42(10) +10 = 430

430-365 =65

 so you save $65 using Company A

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true