A ride-sharing company charges a flat fee of $5.25 for every ride plus a set charge for every mile traveled. A 7-mile ride costs $17.50, while a 12-mile ride costs $26.25.
Let x represent the number of miles traveled. Which expression best models the cost of a ride?

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.

A ride-sharing company charges a flat fee of $5.25 for every ride plus a set charge for every mile traveled. A 7-mile ride costs $17.50, while a 12-mile ride costs $26.25. Let x represent the number of miles traveled. Which expression best models the cost of a ride?

Discover how to model the cost of a ride for a ride-sharing company using a linear equation. This problem involves calculating a flat fee and charge per mile, offering step-by-step solutions with examples of 7-mile and 12-mile rides. Ideal for students in Grades 7-9 learning algebraic concepts.

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