greatwhiteshark said:
Taylor leases cars for $79 per month plus two cents per mile the car is driven up to 72 miles and ten cents per mile over 72 miles. Rachel and Kaitlyn both rented a car from Taylor. In February, Rachel paid $17.82 more than Kaitlyn. How many more miles did Rachel drive?
They BOTH paid the $79: so leave that out.
IF they both drove over 72 miles, then the difference would be divisible
by .10; since difference = 17.82, then K drove less than 72 miles;
and R drove the 72 miles (72 @ .02 = $1.44) plus some @ .10.
k = miles by K, r = miles over 72 by R:
1.44 + .10r - .02k = 17.82
144 + 10r - 2k = 1782 : multiply by 10
simplify to get : y = (x + 819) / 5
That gives 15 solutions (x:y) :
1 164
6 165
11 166
...
71 178
As example, take the last one:
71 @ .02 = 1.42
1.44 + 178 @ .10 = 19.24
19.24 - 1.42 = 17.82
All others work out similarly.
