A taxi company charges $2.25 for the first mile and then $0.20 per mile for each additional mile, or F = $2.25 + $0.20 (m - 1) where F is the fare and m is the number of miles. If Juan's taxi fare was $6.05, how many miles did he travel in the taxi?

F = 2.25 + 0.20 (m-1)

F = 6.05

6.05 = 2.25 + 0.20 (m-1)

Subtract 2.25 on both sides

6.05 - 2.25 = 0.20 (m-1)

3.8 = 0.2 (m-1)

Divide both sides by 0.2

3.8/0.2 = m - 1

19 = m - 1

Add 1 on both sides

19 + 1 = m

m = 20

If Juan's taxi fare was $6.05, then Juan traveled 20 miles in the taxi.

In this problem, it is just a simple case of substitution and solving for the m which is the number of miles. Take the equation F = 2.25 + 0.20 (m-1). According to the given, the fare, or the F is 6.05 so with that, we can already solve the equation. this will be 6.05 = 2.25 + 0.20 (m-1). After that, all we have to do is just solve for the m. If we would solve for the m, we will end up with a final answer of 20. So all in all, the taxi was able to travel 20 miles on the 6.05 fare of Juan