How do I work this out?

[sarahilc]

Airport Taxi charges $6, plus $0.50 per kilometer.
Airport Limo charges a flat rate of $40 for its limousine service.
Write a system of equations that describes the cost and then solve.

so I have
x+y=40
x6+.50y=40?
I don't think that's right, plus I have to simplify it and stuff to solve it... :?

 

[Loren]

There is no way I can help you until you identify what x stands for and what y stands for. In all word problems, you will do better if you define what the variables represent BEFORE you write the equations. Write them down. In this case you have to recognize that the Airport Taxi's total charge will be determined by how many kilometers is traveled. Maybe you should start by making the statement "Let x represent the number of km traveled by the Airport Taxi." Then you can make the statement that the total cost charged by the Airport Taxi is 6+0.5x. Maybe you would want to call that y. Possibly you could solve the problem using only the one variable. Try to go from here. After giving it a good try, if you need more help, come back.

I had to leave for a minute. I'm back and upon analyzing further, I'm wondering if you have presented the entire problem. Are you dealing with equations or inequalities?

It seems to me you will end up with three statements...

If the distance traveled is less than so many km, then Airport Taxi is the cheapest.
If distance traveled is so many km, then the charges of the two companies are equal.
If the distance traveled is greater than so many km, then Airport Limo is the cheapest.

Your job is to determine the measure of "so many km".

Maybe I'm missing something???

 

[sarahilc]

Actually that just totally helped, I was just having a bit of a mental block.
no, I hadn't written the whole question, it starts:
Darrell is making arrangements to pick up a client at the airport. (And then the rest that I previously wrote)
a) write as a system of equations
b) solve the system you wrote in a
v) explain what the solution to the system represents
d) which is cheaper
Let x represent number of kilometers traveled.
Let y represent total cost of transportation.

Taxi:
y=6+0.5x
Limo:
y=40
when graphed, those intersect at 68.
So the taxi is cheaper than the limo until 68km, when they are the same amount. Further than 68km and the taxi is cheaper, so the cost would depend on how far the airport was from the other destination.
Just jotting it down roughly, does that sound about right?