Question 1160253: 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?
Answer by greenestamps(13203)   (Show Source):
You can put this solution on YOUR website!
The hire fee is fixed, so the difference between the two bills is because of the difference in the number of kilometers.
The difference between the two bills is $16.10; and we know the rate per kilometer is a multiple of $0.10. That means we need to find how to factor $16.10 as the product of a whole number of kilometers and a rate which is a multiple of $0.10.
There is only one way to do that: 7*$2.30.
So the rate per kilometer is $2.30.
Now we use that rate along with the fact that the hire rate is a whole number of dollars to determine the hire rate.
The total for the older bill was $21.80. If that is a whole number of dollars plus some multiple of $2.30, then the number of kilometers had to be 6. So the cost for the distance traveled was 6*$2.30 = $13.80; and that means the hire fee is $21.80-$13.80 = $8.
So her last journey, with a total bill of $37.90, was $8 for the hire and the rest for the distance traveled. $37.90-$8 = $29.90; $29.90/$2.30 = 13.
So the distance for her last journey was 13 kilometers.
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