The cost of taxi calculated using the constraints given include :
Taxi cost :
First [tex] \frac{1}{4} \: of a mile = 2.50 [/tex]
Every additional [tex] \frac{1}{4} = 0.30 [/tex]
Cost of [tex] \frac{1}{5} \: of a mile [/tex]
0.2 miles < 0.25 miles ; hence, cost will equal the cost of first 0.25 miles = $2.5
[tex] \frac{6}{5} = 1 \frac{1}{5} = \frac{1}{4} + 3(\frac{1}{4}) + \frac{1}{5} :\ miles [/tex]
[tex] \frac{1}{5} \: of \: a \: mile[/tex] after the initial distance charged at $2.50 will cost $0.30
Cost of [tex] \frac{6}{5} \: miles [/tex] = 2.50 + 3(0.30) + 0.30 = 3.70
5.80 = 2.50 + (0.3y) ; where, y = number of [tex] \frac{1}{4} \: miles [/tex] after the initial
5.80 - 2.50 = 0.3y
3.30 = 0.3y
Divide both sides by 0.3
y = 3.30 ÷ 0.3 = 11
y = 11
Therefore, distance that can be traveled with $5.80 = [tex] \frac{1}{4} + 11(\frac{1}{4}) = 3 \: miles [/tex]
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