Question

Company A charges a fee of $5 for a cab ride, plus a charge of $0.50 for each mile driven.
Company B charges a fee of $10 for a cab ride, plus a charge of $0.10 for each mile driven.
For what number of miles driven will the cost of a cab ride be the same for both companies?
Enter your answer in the box.

Answer 1

To find the number of miles driven for which the cost of a cab ride will be the same for both companies, we can set up equations for the cost of each company's ride based on the number of miles \( x \).

For Company A, the cost \( C_A \) is given by:

\[
C_A = 5 + 0.50x
\]

For Company B, the cost \( C_B \) is given by:

\[
C_B = 10 + 0.10x
\]

To find the number of miles for which the costs are equal, we set \( C_A \) equal to \( C_B \):

\[
5 + 0.50x = 10 + 0.10x
\]

Next, we will solve for \( x \). First, we can simplify the equation by subtracting \( 0.10x \) from both sides:

\[
5 + 0.50x - 0.10x = 10
\]

This simplifies to:

\[
5 + 0.40x = 10
\]

Next, we subtract 5 from both sides:

\[
0.40x = 5
\]

Now, we divide both sides by 0.40:

\[
x = \frac{5}{0.40} = \frac{5}{0.4} = \frac{5 \times 10}{4} = \frac{50}{4} = 12.5
\]

Thus, the number of miles driven for the cost of a cab ride to be the same for both companies is:

\[
\boxed{12.5}
\]