system of linear equations for: Ace rents cars for $20 plus

[mjh94]

Ace Rent-a-car charges a flat fee of $20 and $.23 a mile for their cars. Acme Rent-a Car charges a flat fee of $40 and $.15 a mile for their cars. After how many miles would Ace become more expensive than Acme.

You must use a system of linear equations.

I don't even know where to start!

 

[stapel]

I don't even know where to start!

Hmmm.... That's awkward. If you have no idea even how to get started, this implies that you've never worked with algebra (the variables and word-problem set-up stuff), which means you need about six months of classes before reaching this point.

Are you wanting to try to do self-study, to attempt this on your own? Or would it be feasible for you to drop down to a lower class (pre-algebra, or beginning algebra, maybe), so you can learn the stuff you need to be able to understand what this is asking of you?

I'll be glad to try to find a sequence of lesson links that might help you in a program of self-study, but I don't want to bury you in URLs, if that's not what you want. When you reply, please specify how far you have gotten in your studies. For instance, did you take any algebra back in high school? And how long ago did you graduate? (I'd forgotten most of what I'd learned by the time I went back to college, too!)

Thank you!

Eliz.

 

[mjh94]

I've done function words problems before but I don't understand how to set this up so I can see when Ace becomes more expensive. I can only think to do guess and check. I would think it would be something like

y= 20+.23x
y=40+.15x

For some reason I just don't think it will give me the answer I am looking for.

 

[cheffy]

Ace Rent-a-car charges a flat fee of $20 and $.23 a mile for their cars. Acme Rent-a Car charges a flat fee of $40 and $.15 a mile for their cars. After how many miles would Ace become more expensive than Acme.

You must use a system of linear equations.I've done function words problems before but I don't understand how to set this up so I can see when Ace becomes more expensive. I can only think to do guess and check. I would think it would be something like
y= 20+.23x
y=40+.15x
For some reason I just don't think it will give me the answer I am looking for.

Find the number of miles when the two companies are charging the same amount of $ (I'm assuming if you've worked with function word problems before you can do this). The next mile after that, one company will charge more than the other.

 

[stapel]

I've done function words problems before but I don't understand how to set this up so I can see when Ace becomes more expensive.

Ah. So you have taken some algebra and you do have some idea how to get started. That's a different kettle of fish entirely! :wink:

You're on the right track with setting up two equations, and you've actually got two equations that'll work -- with some tweaking:

. . . . .y = 20 + 0.23x

. . . . .-20 = 0.23x - y

...and:

. . . . .y = 40 + 0.15x

. . . . .-40 = 0.15x - y

So your "system of equations", in fairly standard form, is:

. . . . .0.23x - y = -20
. . . . .0.15x - y = -40

Whereas, in earlier algebra courses, you would have set your two equations equal to each other:

. . . . .20 + 0.23x = 40 + 0.15x

...and solved for the mileage "x" at which they were equal, now you need to solve the system of equations (provided above) by whatever method(s) they've covered in class and/or in your text. The x-value will be the mileage at which the fees are equal, and the y-value will be the charge for that mileage.

Note: From your earlier study of slopes and graphing linear equations, obviously y = 20 + 0.23x has the steeper slope, and will thus be the "higher" line (and charge) after the intersection point.

Eliz.