We are given that the cost of a ride is composed of a flat fee and a charge per mile. Let’s break this down step by step.

Known information:

• Flat fee: $5.25
• Cost for 7 miles: $17.50
• Cost for 12 miles: $26.25
• $x$: the number of miles traveled

General cost formula:

The total cost $C(x)$ of a ride can be modeled as: $C(x) = \text{flat fee} + \text{cost per mile} \times x$ Thus: $C(x) = 5.25 + r \cdot x$ where $r$ is the cost per mile.

Step 1: Set up equations for the two cases

Using the cost of a 7-mile and a 12-mile ride, we can set up two equations:

1. $17.50 = 5.25 + 7r$
2. $26.25 = 5.25 + 12r$

Step 2: Solve the system of equations

Subtract the flat fee from both sides of each equation:

1. $17.50 - 5.25 = 7r$ → $12.25 = 7r$
2. $26.25 - 5.25 = 12r$ → $21.00 = 12r$

Step 3: Solve for $r$

From the first equation: $r = \frac{12.25}{7} = 1.75$

Step 4: Verify

Plugging $r = 1.75$ into the second equation: $21.00 = 12 \times 1.75 = 21.00$ The value of $r = 1.75$ is correct.

Final Expression:

Thus, the expression for the cost of a ride based on the number of miles traveled $x$ is: $C(x) = 5.25 + 1.75x$

This expression models the cost of a ride.

Do you want any more details or have any questions?

Here are 5 related questions:

1. How would the expression change if the flat fee increased to $6?
2. What would be the cost of a 20-mile ride using this formula?
3. If a ride costs $40, how many miles were traveled?
4. How would the total cost change if the cost per mile doubled?
5. How can you graph this cost function?

Tip: Always break down word problems into equations based on given relationships.