verbal linear equations
posted by tanya on .
a taxi costs $2.75 for the first quarter of a mile and $0.85 for each subsequent quarter mile.A ride that cost $23.15 is how many miles longer than a ride that costs $17.20?(please i don't want example show me how u work it out )

c = 2.75 + .85q
where
c = cost of ride
q = number of 1/4 miles driven
There are two ways you can tackle this. One is to figure the length of each ride:
23.15 = 2.75 + .85q
q = 24 (6 miles)
17.20 = 2.75 + .85q
q = 17 (4.25 miles)
So, the more expensive ride is 1.75 miles longer

The other way is to see that once the initial charge is subtracted, the difference in cost is just .85 times the difference in quartermiles:
(23.152.75) (17.202.75) = .85d
Note how you don't even have to worry about the initial cost, since it cancels out when both charges are the same:
23.1517.20 = .85d
5.95 = .85d
d = 7 quartermiles
or, 1.75 miles difference