Set up and solve an equation for the following business situation.
Pitt's Pit Stop sold $15,700.50 worth of gasoline yesterday. Regular sold for $3.30 a gallon and premium sold for $3.45 a gallon. If the station sold 360 more gallons of regular than premium, answer the following questions.
(a)
How many gallons of each type of gasoline were sold?
regular	  
Incorrect: Your answer is incorrect.
 gal
premium	  
Incorrect: Your answer is incorrect.
 gal
(b)
If the profit on regular gas is $0.15 per gallon and on premium is $0.18 per gallon, what was the station's total profit (in dollars)?
$   

Let's break down and set up the problem in steps:

### Variables:
- Let $ r $ represent the number of gallons of **regular** gas sold.
- Let $ p $ represent the number of gallons of **premium** gas sold.

### Information given:
- Regular gas costs $3.30 per gallon.
- Premium gas costs $3.45 per gallon.
- The station sold $15,700.50 worth of gasoline.
- The station sold 360 more gallons of regular than premium, meaning $ r = p + 360 $.

### Step 1: Set up the total sales equation
The total sales for regular gas is $ 3.30r $ (price per gallon multiplied by gallons sold).
The total sales for premium gas is $ 3.45p $.

Thus, the total sales equation is:

\[
3.30r + 3.45p = 15,700.50
\]

### Step 2: Substitute $ r = p + 360 $ into the sales equation
Substituting for $ r $ in the equation:

\[
3.30(p + 360) + 3.45p = 15,700.50
\]

### Step 3: Solve for $ p $ (premium gallons sold)

First, expand the equation:

\[
3.30p + 1,188 + 3.45p = 15,700.50
\]

Combine like terms:

\[
6.75p + 1,188 = 15,700.50
\]

Subtract 1,188 from both sides:

\[
6.75p = 14,512.50
\]

Now, solve for $ p $:

\[
p = \frac{14,512.50}{6.75} = 2,150
\]

So, the number of **premium gallons** sold is $ p = 2,150 $.

### Step 4: Solve for $ r $ (regular gallons sold)

Now that we know $ p = 2,150 $, we can substitute it into $ r = p + 360 $:

\[
r = 2,150 + 360 = 2,510
\]

Thus, the number of **regular gallons** sold is $ r = 2,510 $.

### (a) Answer:
- Regular gas sold: 2,510 gallons
- Premium gas sold: 2,150 gallons

---

### Step 5: Calculate the total profit
- The profit on regular gas is $0.15 per gallon.
- The profit on premium gas is $0.18 per gallon.

Thus, the total profit can be calculated as:

\[
\text{Profit} = 0.15r + 0.18p
\]

Substitute the values of $ r $ and $ p $:

\[
\text{Profit} = 0.15(2,510) + 0.18(2,150)
\]

Calculate each term:

\[
\text{Profit} = 376.50 + 387 = 763.50
\]

### (b) Answer:
The total profit is **$763.50**.

---

### Do you have any questions, or would you like further details? Here are some related questions to practice:

1. How would the solution change if the prices per gallon were different?
2. What if the station sold 500 more gallons of regular gas instead of 360?
3. How much more profit would the station make if the premium gas profit was $0.20 per gallon?
4. How much gasoline would the station need to sell to reach $20,000 in total sales?
5. What would be the total sales if the station sold equal amounts of regular and premium gasoline?

#### Tip:
Always check if your equations align with the problem's conditions before solving, especially when substituting variables.

Set up and solve an equation for the following business situation. Pitt's Pit Stop sold $15,700.50 worth of gasoline yesterday. Regular sold for $3.30 a gallon and premium sold for $3.45 a gallon. If the station sold 360 more gallons of regular than premium, answer the following questions. (a) How many gallons of each type of gasoline were sold? (b) If the profit on regular gas is $0.15 per gallon and on premium is $0.18 per gallon, what was the station's total profit (in dollars)?

Learn how to solve a business problem involving gasoline sales at Pitt's Pit Stop. This problem demonstrates key algebraic concepts, including setting up and solving linear equations to find the number of gallons sold and calculating total profit. Suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation