Question 1160244: A taxi company charges a fixed hire fee (which is a whole number of dollars) plus a rate for each
kilometer (which is a multiple of 10¢ and more than the set national minimum rate of $1.75),
rounded up to the nearest kilometer.
Maira’s last journey cost $37.90, but she does not know how far it was, or what the fixed hire fee
is. She wants to know how far the journey was.
She has a previous bill from the same taxi company, for a different journey, for $21.80.
How far was her last journey?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A taxi company charges a fixed hire fee (which is a whole number of dollars) plus a rate for each kilometer (which is a multiple of 10¢ and more than the set national minimum rate of $1.75), rounded up to the nearest kilometer.
Therefore min dist: 1.75/.1 = 17.5 ~ 18 km min dist
f(x) = .10x + a
Maira’s last journey cost $37.90, but she does not know how far it was, or what the fixed hire fee is.
x = dist traveled
a = fixed amt
.10x + a = 37.90
a = -.10x + 37.90
She wants to know how far the journey was.
She has a previous bill from the same taxi company, for a different journey, for $21.80.
y = dist traveled in this journey
.10y + a = 21.80
a = -.10y + 21.80
How far was her last journey
:
Using these two equations
.10x + a = 37.90
.10y + a = 21.80
---------------------subtraction eliminates a
.10x - .10y = 16.10
.10x - .10y = 16.10
-.10y = -10x + 16.10
get rid of the neg and decimal mult by -10
y = x - 161
lets assume y = 18 km (min trip)
x - 161 = 18
x = 161 + 18
x = 179 kms
:
see of that gives us our fixed fee
.10(179) + a = 37.90
17.90 + a = 37.90
a = 37.90 - 17.90
a = $20 is the fixed fee
:
See if that checks out with 2nd trip y = 18 km
.10y + a = 21.80
.10(18) + a = 21.80
1.80 + a = 21.80
a = 21.80 - 1.80
a = $20 here too
:
Summarizing
fixed fee = $20
1st trip: 179 km
2nd trip: 18 km
Answer by MathTherapy(10555)  (Show Source):
You can put this solution on YOUR website! A taxi company charges a fixed hire fee (which is a whole number of dollars) plus a rate for each
kilometer (which is a multiple of 10¢ and more than the set national minimum rate of $1.75),
rounded up to the nearest kilometer.
Maira’s last journey cost $37.90, but she does not know how far it was, or what the fixed hire fee
is. She wants to know how far the journey was.
She has a previous bill from the same taxi company, for a different journey, for $21.80.
How far was her last journey?
ANKOR's solution doesn't make sense.
How can the difference in the bills be $16.10 ($37.90 - 21.80), but difference in distance is 161 (179 - 18) km?
The slope or rate is the same for both trips, and based on what's given, is > the MINIMUM of $1.75, and also a MULTIPLE of 10c, or .10.
Additionally, how can a 179-km trip cost $21.80, while an 18-km trip cost $37.90? Any sense in that?
Isn't it QUITE obvious that all of the above make NO SENSE?
I don't know where ANKOR's head was, but these people need to THINK before attempting to help someone with a math problem.
Tutor @Greenestamps worked the problem earlier, so see his solution!
I worked it out and got the same thing Tutor @Greenestamps got: a rate of $2.30 per km, and a fixed rate of $8, thus leading to trip-cost equation: y = 2.3x + 8.
This means, as explained by Tutor @Greenestamps that her last journey was 
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