A business woman intends to rent a car for a 3 day business trip. The rental is $65 a day and $.15 per mile (plan 1) or $90 a day with unlimited mileage (plan 2). She is not sure how many miles she will drive but estimates that it will be between 400 and 800 miles.

A) For each plan find a formula for the cost C in terms of the number of a miles driven
B) Which rental plan is cheaper if she drives 400 miles?
C) Which rental plan is cheaper if she drives 800 miles?
D) At what mileage do the two plans cost the same?
Please help with all of them and show the work step by step. I want to check my answers please.

A

plan1-cost = .15m + 195
plan2-cost = 270
where m is the number of miles

B and C, just plug in the mileages

D
set .15m + 195 = 270 and solve

A)

For plan 1, the cost C in terms of the number of miles driven can be calculated using the formula:
C = 65 * number of days + 0.15 * number of miles

For plan 2, the cost C in terms of the number of miles driven can be calculated using the formula:
C = 90 * number of days

In both formulas, the number of days is fixed at 3 days, as mentioned in the question.

B)
To compare the two plans when she drives 400 miles, we substitute the values into both formulas:

For plan 1:
C = 65 * 3 + 0.15 * 400
= 195 + 60
= 255

For plan 2:
C = 90 * 3
= 270

Therefore, plan 1 is cheaper if she drives 400 miles.

C)
To compare the two plans when she drives 800 miles, we substitute the values into both formulas:

For plan 1:
C = 65 * 3 + 0.15 * 800
= 195 + 120
= 315

For plan 2:
C = 90 * 3
= 270

Therefore, plan 2 is cheaper if she drives 800 miles.

D)
To find the mileage at which the two plans cost the same, we can set the two formulas equal to each other and solve for the number of miles:

65 * 3 + 0.15 * miles = 90 * 3

Simplifying the equation:

195 + 0.15 * miles = 270

Subtracting 195 from both sides:

0.15 * miles = 75

Dividing both sides by 0.15:

miles = 500

So, the two plans cost the same when she drives 500 miles.