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Question

Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.

(7 points)
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Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold.

Response area a + Response area s = Response area

900 tickets are sold for the spring fling. Write an equation to represent this situation.

a + Response area = Response area

Use the above system of equations to determine how many adult and student tickets were sold.

Response area adult tickets and Response area student tickets were sold.

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Answer 1

Let's break down the problem step by step.

Step 1: Write the equation representing ticket sales

You want to express the total revenue generated from the adult and student tickets sold. Adult tickets cost $4 each, and student tickets cost $2.50 each. The total revenue is $2,820.

We are using:

• \( a \) = number of adult tickets sold
• \( s \) = number of student tickets sold

The equation for revenue generated is:

\[ 4a + 2.5s = 2820 \]

Now we place it in the designated response area format:

• Response area a = 4a
• Response area s = 2.5s
• Response area = 2820

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Step 2: Write the equation for the total number of tickets sold

You mentioned that 900 tickets are sold in total. Thus, we set up the following equation:

Total tickets equation:

\[ a + s = 900 \]

Now we place it in the response area format:

• Response area = s
• Response area = 900

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Step 3: System of equations

Now we have the system of equations:

1. \( 4a + 2.5s = 2820 \)
2. \( a + s = 900 \)

Step 4: Solve the system of equations to find the values of \( a \) and \( s \)

From the second equation, we can express \( s \) in terms of \( a \):

\[ s = 900 - a \]

Now substitute \( s \) in the first equation:

\[ 4a + 2.5(900 - a) = 2820 \]

Expanding and simplifying:

\[ 4a + 2250 - 2.5a = 2820 \]

Combining like terms:

\[ 1.5a + 2250 = 2820 \]

Subtracting 2250 from both sides:

\[ 1.5a = 570 \]

Dividing by 1.5:

\[ a = \frac{570}{1.5} = 380 \]

Now substitute back to find \( s \):

\[ s = 900 - a = 900 - 380 = 520 \]

Step 5: Final response

So, the number of adult tickets sold is 380 and the number of student tickets sold is 520.

Thus, we can conclude with the final response:

Response area: 380 adult tickets and 520 student tickets were sold.