SOLUTION: A taxi company charges a fixed cost for the first mile and $1.30 for each additional mile. If it costs $14 to travel 9 miles, how much was the cost of the first mile?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A taxi company charges a fixed cost for the first mile and $1.30 for each additional mile. If it costs $14 to travel 9 miles, how much was the cost of the first mile?      Log On


   

Question 1037211: A taxi company charges a fixed cost for the first mile and $1.30 for each additional mile. If it costs $14 to travel 9 miles, how much was the cost of the first mile?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = number of miles.
f = fixed cost for the first mile.
c = total cost.

total cost = fixed cost for the first mile plus 1.30 * the additional miles.

the formula for that is c = f + 1.30 * (x-1).

you are given that c = 14 and that x = 9.

the formula becomes 14 = f + 1.30 * (9-1).

simplify this equaiton to get 14 = f + 1.30 * 8.

simplify further to get 14 = f + 10.4

subtract 10.4 from both sides of this equation to get 14 - 10.4 = f

solve for f to get f = 14 - 10.4 = 3.6.

the cost for the first mile is 3 dollars and 60 cents.

the formula of 14 = f + 1.30 * 8 becomes 14 = 3.60 + 1.30 * 8 which becomes 14 = 3.60 + 10.4 which becomes 14 = 14, confirming the solution is correct.