Determining the Cheaper Option: Airport Taxi vs. Limousine

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SUMMARY

The discussion centers on comparing the costs of airport taxi and limousine services for client pickups. The taxi charges a base fee of $6.00 plus $0.50 per kilometer, represented by the equation T = 6 + 0.50x. The limousine has a flat rate of $40, represented by L = 40. To determine which option is cheaper, the two equations can be set equal to each other (L = T) to find the distance at which both services cost the same. Below this distance, the taxi is the more economical choice, while above it, the limousine becomes the cheaper option.

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Ericca
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Darrell is making arrangements to pick up a client at the airport. Airport taxi charges $6.00, plus $0.50 per kilometre. Airport limo charges a flat rate of $40 for its limousine service.
a)Write a system of equations that describes the cost of the taxi and limoousine.
b)solve the system you wrote in a
c) Explain what the solution to the system represents.
d) Darrell is trying to decide whether the taxi or the limo is cheaper. What advice would you give Darrell?
 
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Shouldn't this be in the homework section? (And shouldn't you show us what you have already done?)

The equation for the limousine is easy! Letting L be the cost of the limosine and x the distance driven: L= 40, of course.
The equation for the taxi is almost as easy: Letting T be the cost of the taxi and x the distance driven: T= 6+ 0.50x.

b) I have no idea what you mean by "solve the system you wrote in a". In the first place, it's not really a system- it's two separate equations. In the second, what do you want to solve for?

c) Uh, yeah, that's what I'd like you to do!

d) Okay, I suspect that the problem wants you to set L= T in the two equations and solve for x: the distance at which the two costs are the same. Below that distance, the taxi is cheaper, beyond, the limousine is cheaper.
 

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