Using the given jeepney fare formula F(d)= m + a [d - 4], calculate the fare for a trip of 7.5 km if the minimum fare for the first 4 km is Php 8.00, and the additional fare per km is Php 1.50

To calculate the jeepney fare for a trip of 7.5 km using the given formula \( F(d) = m + a[d - 4] \), we can follow these steps:

### Step 1: Understand the formula and given values
- \( F(d) \) represents the fare for a trip of distance \( d \) kilometers.
- \( m \) is the minimum fare for the first 4 km.
- \( a \) is the additional fare per kilometer after the first 4 km.
- \( d - 4 \) represents the distance traveled beyond the first 4 km.

### Step 2: Plug in the given values
- The minimum fare \( m \) for the first 4 km is Php 8.00.
- The additional fare per kilometer \( a \) is Php 1.50.
- The distance \( d \) of the trip is 7.5 km.

### Step 3: Apply the formula
Substitute the values into the formula:
\[
F(7.5) = 8.00 + 1.50[7.5 - 4]
\]

### Step 4: Simplify the calculation
- Calculate the distance traveled beyond 4 km:
  \[
  7.5 - 4 = 3.5 \text{ km}
  \]
- Now multiply this by the additional fare per km:
  \[
  1.50 \times 3.5 = 5.25 \text{ Php}
  \]
- Finally, add this to the minimum fare:
  \[
  F(7.5) = 8.00 + 5.25 = 13.25 \text{ Php}
  \]

### Answer:
The fare for a trip of 7.5 km is **Php 13.25**.

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Would you like further explanation on how this formula works or how to apply it to other distances?

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Here are five follow-up questions:

1. How would the fare change if the additional fare per kilometer increased to Php 2.00?
2. What would the fare be for a trip of exactly 4 km?
3. How does the formula \( F(d) = m + a[d - 4] \) handle trips less than 4 km?
4. What would be the fare for a 10 km trip using the same formula?
5. How does this formula help in calculating fare structures for different types of public transportation?

**Tip**: When dealing with formulas involving a base cost and additional increments, always isolate the incremental part and ensure you're calculating only for the extra portion beyond the base.

Learn how to calculate the jeepney fare for a trip of 7.5 km using the formula F(d) = m + a[d - 4]. Understand the minimum fare and additional cost per kilometer. Suitable for students in Grades 5-6.

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