A gas station sells regular gasoline for $2.39 per gallon and premium gasoline for $2.79 per gallon. If the gas station sold a total of 550 gallons of both types of gasoline in one day for a total of $1.344.50. how many gallons of premium gasoline were sold?

Options

A. `25`
B. `75`
C. `175`
D. `475`

Answer

To solve the problem step-by-step, we will set up a system of equations based on the information given.

### Step 1: Define Variables
Let:
- \( x \) = number of gallons of regular gasoline sold
- \( y \) = number of gallons of premium gasoline sold

### Step 2: Set Up the Equations
From the problem, we know:
1. The total gallons sold is 550:
\[ x + y = 550 \]
2. The total revenue from the sales is $1,344.50:
\[ 2.39x + 2.79y = 1344.50 \]

### Step 3: Solve for One Variable
From the first equation, we can express \( x \) in terms of \( y \):
\[ x = 550 - y \]

### Step 4: Substitute into the Second Equation
Now, substitute \( x \) in the second equation:
\[ 2.39(550 - y) + 2.79y = 1344.50 \]

### Step 5: Distribute and Simplify
Distributing \( 2.39 \):
\[ 1314.50 - 2.39y + 2.79y = 1344.50 \]
Combine like terms:
\[ 1314.50 + 0.40y = 1344.50 \]

### Step 6: Isolate the Variable \( y \)
Now, isolate \( y \):
\[ 0.40y = 1344.50 - 1314.50 \]
\[ 0.40y = 30 \]

### Step 7: Solve for \( y \)
Divide both sides by 0.40:
\[ y = \frac{30}{0.40} = 75 \]

### Conclusion
Thus, the number of gallons of premium gasoline sold is:
\[ \boxed{75} \]