Question

A taxi driver charges for a ride at a rate of $2$ dollars for the first half mile and $75$ cents for each additional half mile. Which of the following expressions represents the total charge, in cents for $p$ miles, where $p$ is a positive integer?

• A. $25(6p+8)$
• B. $25(6p+5)$
• C. $25(3p+5)$
• D. $1.25+1.5p$
• E. $2+0.75(p-1)$

Answer 1

Answer: (B)

$25(6p+5)$

The charge for a taxi ride in a certain city is $2$ dollars for the first half of a mile and $75$ cents for each additional half of a mile.

Then the charges for $\frac{1}{2}$ miles are $2$ dollars $=200$ cents

When taxi rides $p$ miles:

Given that the charges for additional half mile is $75$ cent.

So for $1$ mile $=150$ cent

Then charges = $200+\left[(p-\frac{1}{2})150\right]$

$=200+\left(\frac{2p-1}{2}\right)150$

$=200+150p-75$

$=150p+125$

$=25(6p+5)$