A car starts a trip with 20 gallons of gasoline in its tank and consumes gas at a rate of 1 gallon for each 25 miles traveled.

Answer

To solve the problem step by step, we need to determine how much gasoline is left in the car after traveling a certain distance, \( x \) miles.

### Step 1: Understand the fuel consumption rate
The car consumes gasoline at a rate of 1 gallon for every 25 miles traveled. This means that for every mile, the car uses:
\[ \text{Gasoline used per mile} = \frac{1 \text{ gallon}}{25 \text{ miles}} = \frac{1}{25} \text{ gallons per mile} \]

### Step 2: Calculate the gasoline consumed for \( x \) miles
If the car travels \( x \) miles, the total amount of gasoline consumed can be calculated by multiplying the distance traveled by the gasoline consumption rate:
\[ \text{Gasoline consumed for } x \text{ miles} = x \times \frac{1}{25} = \frac{x}{25} \text{ gallons} \]

### Step 3: Determine the initial amount of gasoline
The car starts with 20 gallons of gasoline in its tank.

### Step 4: Calculate the remaining gasoline after traveling \( x \) miles
To find the amount of gasoline left in the tank after traveling \( x \) miles, we subtract the gasoline consumed from the initial amount:
\[ G(x) = 20 - \frac{x}{25} \]
where \( G(x) \) represents the amount of gasoline left after traveling \( x \) miles.

### Final Expression
Thus, the formula for the amount of gasoline left in the car after traveling \( x \) miles is:
\[ G(x) = 20 - \frac{x}{25} \]

---