https://file.aiquickdraw.com/mathbot/file/1727444310735j6jdp9zi.jpg

Let's break down and solve each part of the problem from the image.

### Part (a)
**Question:**
Write an equation to represent the amount of gas in Troy’s truck after driving a certain number of miles (assuming he starts with a full tank). Define your variables.

**Solution:**
1. **Define the variables:**
   - Let \( G \) represent the amount of gas remaining in the tank (in gallons).
   - Let \( m \) represent the number of miles driven.

2. **Equation:**
   Troy's truck gets 21 miles per gallon. Therefore, for every mile driven, the truck uses \( \frac{1}{21} \) gallons of gas.

   If Troy starts with a full tank of 30 gallons, the amount of gas used after driving \( m \) miles is \( \frac{m}{21} \) gallons.

   The remaining gas in the tank, \( G \), is then given by:
   \[
   G = 30 - \frac{m}{21}
   \]

### Part (b)
**Question:**
If the tank is half full, approximately how many miles has Troy driven since last filling up his tank?

**Solution:**
1. A half-full tank means there are 15 gallons left in the tank.
2. Set \( G = 15 \) in the equation from part (a) and solve for \( m \):
   \[
   15 = 30 - \frac{m}{21}
   \]
   \[
   \frac{m}{21} = 30 - 15
   \]
   \[
   \frac{m}{21} = 15
   \]
   \[
   m = 15 \times 21 = 315
   \]

Therefore, Troy has driven approximately **315 miles** since the last filling up his tank.

Would you like more details or have any questions?

### Related Questions:
1. If Troy drives 100 miles, how much gas will he have left in his tank?
2. How many gallons of gas does Troy use after driving 200 miles?
3. What is the maximum number of miles Troy can drive on a full tank?
4. If Troy drives 50 miles per day, how many days will it take for his tank to become empty?
5. How would the equation change if Troy's truck averaged 25 miles per gallon instead of 21?

**Tip:** To find the number of gallons used, divide the miles driven by the miles per gallon.

Troy's truck has a 30 gallon gas tank and gets an average of 21 miles per gallon. a) Write an equation to represent the amount of gas in Troy’s truck after driving a certain number of miles (assuming he starts with a full tank). Define your variables. b) If the tank is half full, approximately how many miles has Troy driven since last filling up his tank?

Solve a linear equation problem involving a truck with a 30-gallon gas tank and an average fuel efficiency of 21 miles per gallon. Learn how to represent gas usage with an equation and find out how many miles Troy has driven when his tank is half full.

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