First we will write the equation and then determine the number of miles we traveled if a ride cost $7.75.
Writing an Equation
Let's assume that the minimum number of miles we have to pay for is 18 mile. This means that $1.75 can be treated as a fixed cost F.
F= 1.75If we pay more than F, the cost will depend on the number of miles we travel above the first 18 mile. The taxi charges $0.30 for each additional 18 mile However, since one-eighths of one mile is an awkward unit to work with, we will convert this to a per-mile cost by multiplying 0.3 by 8.
1mile charge: $0.30* 8=$2.4
This means that for each additional 1 mile, the taxi charges $ 2.4.
We can now create an algebraic expression that describes the variable cost V in terms of the number of miles m. Note that the first 18 mile we travel is payed for by the fixed cost.
V = 2.4 (m-1/8)
Now we can write the equation for the cost c which is the sum of the fixed and variable cost.
c= F+ V
⇓
c= 1.75+ 2.4 (m-1/8)
Finding the Number of Miles
To find how many miles we traveled if a ride costs $7.75, we substitute c= 7.75 in the equation and solve for m.
