Question 1016897: It costs $3 a mile to go for a ride in a taxi. After 6 miles, it then costs $5.25 per mile. Write the particular equation expressing cost (c) in miles (d).
This is supposed to be written as ONE equation?!
Found 2 solutions by Theo, MathTherapy:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let c = total cost.
let d = number of miles.
it cost 3.00 per mile up to 6 miles.
it costs 5.25 per mile after 6 miles.
as a split equation, this would be:
c = 3.00 * d, 0 <= d <= 6
c = 5.25 * d - 13.5, d > 6
i don't believe it can be modeled as one equation.
it's more than likely 2 equations.
i call these split equations.
i think they're also called partial equations.
different equations take care of different parts of the problem.
in the real world, problems like this are usually solved by computer.
the computer contains logic that can differentiate between whether or not the number of miles traveled was less than or equal to 6, or greater than 6.
an example of pseudo code (computer code written in english) shows you what i mean.
if the number of miles traveled is less than or equal to 6, charge 3 dollars per mile.
if the number of miles traveled is greater than 6, charge 5.25 per mile and subtract 13.5 dollars from the total.
13.5 is equal to 6 * 2.25.
that's the difference between 5.25 dollars per mile and 3 dollars per mile.
so, the first 6 miles are charged at 5.25 dollars per mile minus 2.25 dollars per mile for a net charge of 3 dollars per mile.
after 6 miles, the full 5.25 dollars per mile is charged.
here's what would happen.
miles traveled cost
0 3 * 0 = 0
1 3 * 1 = 3
2 3 * 2 = 6
3 3 * 3 = 9
4 3 * 4 = 12
5 3 * 5 = 15
6 3 * 6 = 18
7 5.25 * 7 - 13.5 = 23.25
8 5.25 * 8 - 13.5 = 28.5
when you go 7 miles, it's 3 dollars per mile for the first 6 plus 5.25 for the next mile which is equal to 18 + 5.25 = 23.5 dollars.
when you go 8 miles, it's 3 dollars per mile for the first 6 plus 5.25 for the next 2 miles which is equal to 18 + 2 * 5.25 = 18 + 10.5 = 28.5.
the algebraic formula that takes that into account was shown above and is reproduced here:
c = 3.00 * d, 0 <= d <= 6
c = 5.25 * d - 13.5, d > 6
these formulas say:
charge 3 dollars per mile when the number of miles is less and or equal to 6.
charge 5.25 dollars per mile and then subtract 13.5 dollars from the total when the number of miles is greater than 6.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
It costs $3 a mile to go for a ride in a taxi. After 6 miles, it then costs $5.25 per mile. Write the particular equation expressing cost (c) in miles (d).
This is supposed to be written as ONE equation?!
Piece-wise function, with: 
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