In a large city, taxicabs charge $1.00 for the first 1:5 mile and $0.36 for each additional 1:5 mile. Frank has only 9.50. What is the maximum distance he can travel (not including a tip for the cabbie) ?

Frank can travel 4.8 mi.

The cabbie measures the distance in fifths of a mile. Let's say that Frank travels n fifths.

The charge (C) is $1.00 for the first fifth and $0.36 for the remaining (n - 1) fifths.

C = 1.00 + 0.36 (n-1)

C = 1.00 + 0.36n - 0.36 = 0.64 + 0.36n.

If Frank can spend only $9.50,

9.50 = 0.64 + 0.36n

0.36n = 9.50 - 0.64 = 8.86

n = 8.86/0.36 = 24.6

If the meter "pulses" after each fifth, Frank can travel only an integral number of fifths (24).

Frank can travel 24 * ¹/₅ mi = 4.8 mi

Check: $1 + $0.36*23 = $9.28. Frank will have $0.22 left over, not enough for another fifth-mile.