Question

A cab ride costs $\$3.25$ for the first half mile and $\$0.70$ for each mile after the first – half mile. How far can someone travel for $\$12$?
a. 9 miles
b. 13.5 miles
c. 14.5 miles
d. 26 miles
e. 27 miles

Answer 1

Hint:To solve this question, we will be following the steps which are given below.
Let us assume that the number of half – miles that can be travelled in $\$12$ to be ‘x’.
So now, we shall form an equation by which we will be able to solve this question.
The equation is given as follows:-
\[\Rightarrow 3.25\ \ +\ \ 0.7x\ \ -\ \ 0.7\ \ =\ \ 12\]

Complete step-by-step answer:
Let us now solve this question.
Cost of cab ride of first half – mile = $\$3.25$
Cost of each mile after the first half – mile = $\$0.70$
We know that the number of half – miles that can be travelled is assumed as ‘x’.
Let us now solve the equation that is mentioned in the hint provided above.
\[\Rightarrow 3.25\ \ +\ \ 0.7x\ \ -\ \ 0.7\ \ =\ \ 12\]
According to the given question,
\[\begin{align}
  & \Rightarrow 3.25\ \ +\ \ 0.70\ \left( x-1 \right)\ \ =\ \ 12 \\
 & \Rightarrow 3.25\ \ +\ \ 0.7x\ \ -\ \ 0.7\ \ =\ \ 12 \\
 & \Rightarrow 3.25\ \ -\ \ 0.7\ \ +\ \ 0.7x\ \ =\ \ 12 \\
 & \Rightarrow 2.55\ \ +\ \ 0.7x\ \ =\ \ 12 \\
 & \Rightarrow 0.7x\ \ =\ \ 12\ \ -\ \ 2.55 \\
 & \Rightarrow 0.7x\ \ =\ \ 9.45 \\
 & \Rightarrow x\ \ =\ \ \dfrac{9.45}{0.7} \\
 & \Rightarrow x\ \ =\ \ 13.5 \\
\end{align}\]
So, as per the calculations, the answer of this question is 13.5 miles.
Hence, the total miles that can be travelled for $\$12$ are 13.5 miles.
Therefore, the correct option for this question is (b) 13.5 miles.

Note:One needs to form an equation to solve this question. It will make the calculations easier and shorter. If an equation is not formed, then the calculations will be lengthy and time consuming.Also, the calculations must be done carefully as any mistake in the calculus can affect the answer.