Question

Rob took a taxi to reach a certain destination. The taxi service charges $\$1\frac{1}{5}$ as a fixed charge for any ride and $\$1\frac{3}{5}$ per mile with a $25\%$ discount on the total cost. How far can Rob travel for $\$12$?

• A. $9\frac{1}{4}$ miles
• B. $6$ miles
• C. $9$ miles
• D. $6\frac{1}{4}$ miles

Answer 1

The correct option is A $9\frac{1}{4}$ miles

Fixed charges of taxi service $\$1\frac{1}{5}$

Per mile charge $=\$1\frac{3}{5}$

Total cost to travel $“n”$ miles $=n\times$ Cost per mile + Fixed charges of taxi service - Discount

$12=n\times 1\frac{3}{5}+1\frac{1}{5}-\frac{25}{100}\times$ Total cost of travel without discount

$12=n\times \frac{8}{5}+\frac{6}{5}-\frac{1}{4}\times (n\times \frac{8}{5}+\frac{6}{5})$

$12=1.6n+1.2-\frac{1}{4}\times (1.6n+1.2)$

$12=1.6n+1.2-0.4n-0.3$

$12=1.2n+0.9$

$12-0.9=1.2n$

$11.1=1.2n$

$n=\frac{11.1}{1.2}$

$n=\frac{111}{12}$

$n=9\frac{3}{12}$

$n=9\frac{3}{12}$

$n=9\frac{1}{4}$ miles

Rob can travel a total of $9\frac{1}{4}$ miles.