Question

An Uber fare in Columbus is $3.50 for the first ½ mile and additional mileage charged at a rate of $0.30 for each additional 0.1 mile. You plan to give the driver a $2 tip. How many miles can you ride for $15? Please show or explain your calculations.

Answer 1

If we consider the first half mile to be charged at $0.30 per tenth also, that half-mile costs $1.50 and the charges amount to a fixed fee of $2.00 and a variable fee of $0.30 per tenth mile.

After you subtract the $2 tip and the fixed $2 fee from the trip budget amount, you have $11.00 you can spend on mileage charges. At 0.30 per tenth mile, you can travel

... $11.00/$0.30 = 36 2/3 . . . . tenth-miles

The trip is measured in whole tenths, so you can ride ...

... 36 × 1/10 = 3.6 miles

_____

If you want to see this in the form of an equation, you can let x represent the miles you can travel. Then your budget amount gives rise to the inequality ...

... 3.50 + 0.30((x -.50)/0.10) + 2.00 ≤ 15.00

... 3.50 + 3x -1.50 +2.00 ≤15.00 . . . . . . . eliminate parentheses

... 3x ≤ 11.00 . . . . . . . . . . . . . . . . . . . . . . . . collect terms, subtract 4

... x ≤ 11/3 . . . . . . . . . . . . . . . . . . . . . . . . . . divide by 3

... x ≤ 3.6 . . . . . rounded down to the tenth