Respuesta :
Answer:
[tex]\frac{11}{3}[/tex] miles
Step-by-step explanation:
Let the total miles traveled be x.
Now, for the first 0.5 miles total charge is = $3.50
Then, the remaining distance to be traveled[tex]=(x-0.5)[/tex] miles
For each additional 0.1 mile, the additional charge is $0.30
So, for [tex](x-0.5)[/tex] miles, the total additional charge will be[tex]=\frac{0.3}{0.1}(x-0.5) =3(x-0.5)[/tex]
Then, including the $2 tip, the total fare will be[tex]=3.50+3(x-0.5)+2[/tex]
Now, given that total fare is $15, so,
[tex]3.50+3(x-0.5)+2=15\\3.50+3x-1.5+2=15\\3x+4=15\\3x=11\\x=\frac{11}{3}[/tex]miles
Let's assume, total number of miles traveled after the first 0.5 mile are x.
For 0.1 mile, the cost is $0.30
[tex]0.1\times 10 = 1 mile[/tex]
Hence, for 10 miles, cost is
[tex]0.30\times 10 = 3[/tex] dollars
Total amount incurred = $ 3.50 (fixed cost) + 3x (cost per mile) + 2( tip)
He gave a total of $ 15, hence
[tex]15=3.50+3x+2[/tex]
[tex]9.5=3x[/tex]
[tex]x=\frac{95}{30} =\frac{19}{6}[/tex] miles
Total miles traveled = [tex]\frac{19}{6} +\frac{1}{2}[/tex] =[tex]\frac{11}{3}[/tex] miles
