# verbal linear equations

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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 )

• verbal linear equations -

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 quarter-miles:

(23.15-2.75)- (17.20-2.75) = .85d
Note how you don't even have to worry about the initial cost, since it cancels out when both charges are the same:
23.15-17.20 = .85d
5.95 = .85d
d = 7 quarter-miles
or, 1.75 miles difference

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