Question

Yellow Cab Taxi charges $\$1.75$ flat rate in addition to $\$0.65$ per mile. John has only $\$10$ to spend on a ride. Which of the following inequalities describes the distance John can travel?

• A. $0\le x\le 12\frac{9}{13}\text{miles}$
• B. $x\le 11\frac{5}{13}\text{miles}$
• C. $x<12\frac{9}{13}\text{miles}$
  
• D. $0<x<11\frac{5}{13}\text{miles}$

Answer 1

The correct option is A $0\le x\le 12\frac{9}{13}\text{miles}$

Fixed cab charges $=\$1.75$
Cost per mile $=\$0.65$
Let x be the distance traveled by John.
Total charge $=0.65x+1.75$
John has only $\$10$ to spend on the ride. If he hires a cab, he has to pay a minimum of $\$1.75$.
Therefore
$1.75\le 0.65x+1.75\le 10$
$1.75-1.75\le 0.65x+1.75-1.75\le 10-1.75$ (subtracting 1.75 throughout)
$0\le 0.65x\le 8.25$
$0\le x\le \frac{8.25}{0.65}$ (dividing throughout by 0.65)
$0\le x\frac{825}{65}$
$0\le x\le \frac{165}{13}$
$0\le x\le 12\frac{9}{13}$ miles
With the amount of money John has, he can travel 0 to $12\frac{9}{13}\text{miles}.$