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.
