Parker owns a food truck that sells tacos and burritos. He sells each taco for $4.50 and each burrito for $6.75. Yesterday Parker made a total of $576 in revenue from all burrito and taco sales and there were twice as many burritos sold as there were tacos sold. Write a system of equations that could be used to determine the number of tacos sold and the number of burritos sold. Define the variables that you use to write the system.

Let's define the variables:

• Let \( T \) represent the number of tacos sold.
• Let \( B \) represent the number of burritos sold.

From the problem statement, we have the following information:

1. The price of each taco is $4.50.
2. The price of each burrito is $6.75.
3. Total revenue from taco and burrito sales is $576.
4. The number of burritos sold is twice the number of tacos sold.

Using these details, we can set up the following system of equations:

1. The revenue equation can be expressed as: \[ 4.50T + 6.75B = 576 \]

2. The relationship between tacos and burritos can be expressed as: \[ B = 2T \]

So the system of equations is:

\[ \begin{cases} 4.50T + 6.75B = 576 \ B = 2T \end{cases} \]

Apologies for the confusion! Here’s the complete system of equations based on the information provided:

Let:

• \( T \) = number of tacos sold
• \( B \) = number of burritos sold

System of Equations:

1. Revenue Equation: \[ 4.50T + 6.75B = 576 \]

2. Relationship Between Tacos and Burritos: \[ B = 2T \]

Now we have the system of equations:

\[ \begin{cases} 4.50T + 6.75B = 576 \quad \text{(1)} \ B = 2T \quad \text{(2)} \end{cases} \]

This system can be used to solve for the number of tacos and burritos sold.

Certainly! Here it is presented clearly:

Let:

• \( T \) = number of tacos sold
• \( B \) = number of burritos sold

System of Equations:

1. Revenue Equation: \[ 4.50T + 6.75B = 576 \]

2. Relationship Between Tacos and Burritos: \[ B = 2T \]

Final System of Equations:

\[ \begin{cases} 4.50T + 6.75B = 576 \quad \text{(1)} \ B = 2T \quad \text{(2)} \end{cases} \]

This system can be used to determine the number of tacos and burritos sold by Parker.