California round trip

[charger82rt]

Rent-A-Dent (RAD) has rental specials on compact cars:
a. Hondas rent for $25 per day and $.24 (24 cents) per mile.
b. Toyotas rent for $31 per day and $.19 (19 cents) per mile.
? Write a cost equation for each rental car
? The distance from Monterey, Ca to San Francisco, Ca is about 110 miles. Which car would be the better choice to rent for a one-way drive to San Francisco from Monterey?
? Which car would be the better choice to rent for a round-trip drive from Monterey to San Francisco and back?
? What is the break-even point for both rental cars, include the mileage and cost.

1)
Honda = $25 dollars per day and 24 cents per mile (25 multiplied by .24 per mile)
Toyota = $31 dollars per day and 19 cent per mile (31 multiplied by .19 per mile)

2)
The distance from Monterey, Ca to San Francisco is approx. 110 mile

Honda = $25 plus .24 multiplied by 110 which equals 51.4 (25 + 26.4)

Toyota = $31 plus .19 multiplied by 110 which equals 51.9 (20.9 + 31)

The Honda would be a better choice for a one way trip

3)
For a round-trip the Honda would be the best choice because a round trip for both vehicles would give you

Honda = 51.4 multiplied by 2 = 102.8

Toyota = 51.9 multiplied by 2 = 103.8

4) I am unsure how to get this last part done.

 

[tkhunny]

1)
Honda = $25 dollars per day and 24 cents per mile (25 multiplied by .24 per mile)
Toyota = $31 dollars per day and 19 cent per mile (31 multiplied by .19 per mile)

You have just rewritten the given information. You have not written an equation. Define necessary variables and write an equation. Less words.

D = Number of Days Rented
M = Number of Miles Driven
H = Cost of renting the Honda
T = Cost of renting the Toyota

H = $25*D + $0.24*M
T = $31*D + $0.19*M

 

[sgtpepper]

1).
Rental Cost for Honda: Cost = 25 + 0.24x, where x equals the miles driven
Rental Cost for Toyota: Cost = 31 + 0.19x, where x equals the miles driven

2).
Just plug the number of miles driven (110) in for x in your handy dandy equation you made in part 1. See which car gets you there with a smaller cost.

http://tinyurl.com/2p48h3

3).
A round trip would mean going to San Francisco, then back to Monterey, which would be a distance of 110+110 miles, or 220 miles. Using this distance, do the same thing you did in step 2.

http://tinyurl.com/2nj6fq

4).
I believe what it means by break-even point is the point (meaning the number of miles) at which the two cars' rental costs are the same, to do this, you have to set the two equations equal to each other, like so:

25 + 0.24x = 31 + 0.19x

then solve for x:

0.24x = 6 + 0.19x
0.05x = 6
x = 6/0.05
x = 120

http://tinyurl.com/39w9lh

Therefore, when the two cars have traveled 120 miles, their rental costs are the same. (Hint: try plugging it into your equation and see if this is true!)
Hope this helps you; I'm sorry ahead of time if I made any errors.

 

[sgtpepper]

Also, your round trip values are incorrect because you're multiplying the whole value (from part 1) by 2. This means that your are including the daily cost of 25 or 31 in that value - you shouldn't. The daily cost only counts once unless the round trip was made in two (or more) days.