Tanya took a cab from her home to the airport. Her total fare including a tip of $5.00, was $28.50. EZ Cab Company has a pick-up-at-home charge of $2.50, which is not shown on the meter. The cab meter charges $1.00 for the first 0.2 mile and $0.25 for each additional 0.2 mile traveled. With this information, my question is: How much did the cab meter show when Tanya arrived at the airport?

16.2 miles.

Since she paid a $5 tip, the cost for her fare was $23.50.  Let x be the number of 0.2-mile increments in the trip:
23.50 = 2.50 + 1 + 0.25(x-1)

This equation comes from the 2.50 home pick-up fee; $1 for the first 0.2-mile increment; and 0.25 for each other 0.2-mile increment.

Using the distributive property, we have:
23.50 = 2.50 + 1 + 0.25*x - 0.25*1
23.50 = 2.50 + 1 + 0.25x - 0.25

Combining like terms,
23.50 = 0.25x + 2.75

Subtracting 2.75 from both sides, we have:
23.50 - 2.75 = 0.25x + 2.75 - 2.75
20.25 = 0.25x

Dividing both sides by 0.25, we have:
20.25/0.25 = 0.25x/0.25
81 = x

This means there are 81 0.2-mile increments in her trip.  81(0.2) = 16.2 miles