Question

If the driver charges $4$ for the first $\frac{1}{4}$ mile, plus $1.50$ for each additional $\frac{1}{2}$ mile, then the inequality which represents the number of miles $m$, that you could ride and pay no more than $10$ is

• A. $3.25+1.5m\le 10$
• B. $3.25+3m\le 10$
• C. $4+1.5m\le 10$
• D. $4+3m\le 10$

Answer 1

Answer: (B)

$3.25+3m\le 10$

Since the number of miles traveled is $m$ and according to the condition, the driver charges. We can write the total charge as under:

$\$4+\frac{(m-\frac{1}{4})}{\frac{1}{2}}\times \$1.50\le 10$

$\Rightarrow \$4+2(m-\frac{1}{4})\times$ 1.50 \leq 10$

$\Rightarrow 4+3m-\frac{3}{4}\le 10$

$\Rightarrow 3m+3.25\le 10$