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Let's break down the problem step by step based on the images provided.

### Part A:
**Question:**
How much does it cost to drive 100 miles if your car gets 25 miles per gallon and gasoline costs 340 cents per gallon?

**Solution:**
We will use the following relationship to calculate the cost:

\[
\text{Cost} = \left( \frac{\text{Distance Driven}}{\text{Miles per Gallon}} \right) \times \text{Cost per Gallon of Gasoline}
\]

Where:
- Distance Driven = 100 miles
- Miles per Gallon = 25 mpg
- Cost per Gallon of Gasoline = 340 cents (or \$3.40)

Step-by-step:
1. **Calculate the number of gallons needed**:
   \[
   \frac{100 \text{ miles}}{25 \text{ miles per gallon}} = 4 \text{ gallons}
   \]
   
2. **Multiply by the cost per gallon**:
   \[
   4 \text{ gallons} \times 3.40 \text{ dollars per gallon} = 13.60 \text{ dollars}
   \]

So, the cost to drive 100 miles is **\$13.60**.

---

### Part B:
**Question:**
Find a formula that gives the cost $ C $ as a function of the gas mileage $ m $, cost per gallon $ g $, and distance driven $ d $.

**Solution:**
We can generalize the relationship from part A.

The formula for the cost $ C $ to drive a certain distance is:

\[
C = \left( \frac{d}{m} \right) \times g
\]

Where:
- $ d $ = distance driven (in miles)
- $ m $ = miles per gallon (fuel efficiency)
- $ g $ = cost of gasoline per gallon (in dollars)

### Units:
- $ C $ (cost) is in dollars.
- $ d $ (distance) is in miles.
- $ m $ (mileage) is in miles per gallon.
- $ g $ (gas cost) is in dollars per gallon.

---

### Part C:
**Question:**
Use functional notation to show the cost of driving a car that gets 28 miles per gallon, for a distance of 138 miles, if gasoline costs \$3.69 per gallon. Use the formula from part B to calculate the cost.

**Solution:**
Using the formula from part B:

\[
C(d, m, g) = \left( \frac{d}{m} \right) \times g
\]

Given:
- $ d = 138 \text{ miles} $
- $ m = 28 \text{ miles per gallon} $
- $ g = 3.69 \text{ dollars per gallon} $

Step-by-step:
1. **Calculate the number of gallons needed**:
   \[
   \frac{138 \text{ miles}}{28 \text{ miles per gallon}} = 4.93 \text{ gallons}
   \]

2. **Multiply by the cost per gallon**:
   \[
   4.93 \text{ gallons} \times 3.69 \text{ dollars per gallon} = 18.19 \text{ dollars}
   \]

So, the cost to drive 138 miles is **\$18.19**.

---

Would you like more details or further explanation?

Here are 5 related questions:
1. How would the formula change if we included a toll cost per mile?
2. What happens to the cost if the car's efficiency increases to 40 miles per gallon?
3. If the cost of gasoline rises to \$4 per gallon, how would that affect a 100-mile trip?
4. How would you calculate the cost for a round-trip journey of 200 miles with the same gas prices?
5. What would the cost be if gasoline costs 350 cents per gallon and the distance driven is 150 miles?

**Tip:** Always double-check the units when solving word problems involving costs or rates, especially when they involve different systems like miles, gallons, or cents!

How much does it cost to drive 100 miles if your car gets 25 miles per gallon and gasoline costs 340 cents per gallon?

Learn how to calculate the cost of driving 100 miles with a car that gets 25 miles per gallon of gasoline, costing 340 cents per gallon. Follow step-by-step to solve using proportions and basic multiplication. Perfect for students in Grade 8-10.

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