Two types of tickets were sold for a concert held at an amphitheater. Tickets to sit on a bench during the concert cost $75 each, and tickets to sit on the lawn during the concert cost $40 each. Organizers of the concert announced that 350 tickets had been sold and that $19,250 had been raised through ticket sales alone. Which of the following systems of equations could be used to find the number of tickets for bench seats, B, and the number of tickets for lawn seats, L, that were sold for the concert?

Options

A. (75B)(40L)=1,950
B+L=350
B. 40B + 75L = 19,250
B+L=350
C. 75B + 40L =350
B+L=19,250
D. 75B+40L=19,250
B+L=350

Explanation

To solve the problem, we need to set up a system of equations based on the information provided about the ticket sales for the concert.

### Step 1: Define the Variables
Let:
- \( B \) = number of bench tickets sold
- \( L \) = number of lawn tickets sold

### Step 2: Set Up the First Equation
According to the problem, the total number of tickets sold is 350. This can be expressed as:
\[ B + L = 350 \]
This equation represents the total number of tickets sold.

### Step 3: Set Up the Second Equation
Next, we need to account for the total revenue generated from ticket sales. The revenue from bench tickets is \( 75B \) (since each bench ticket costs $75) and the revenue from lawn tickets is \( 40L \) (since each lawn ticket costs $40). The total revenue is given as $19,250. This can be expressed as:
\[ 75B + 40L = 19250 \]
This equation represents the total revenue generated from ticket sales.

### Step 4: Write the System of Equations
Now we have a system of two equations:
1. \( B + L = 350 \)
2. \( 75B + 40L = 19250 \)

### Conclusion
The system of equations that can be used to find the number of tickets for bench seats \( B \) and the number of tickets for lawn seats \( L \) sold for the concert is:
\[ \begin{align*} B + L &= 350 \\ 75B + 40L &= 19250 \end{align*} \]