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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)
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.
Question 1: ___ a + ____ s = _____
900 tickets are sold for the spring fling. Write an equation to represent this situation
a+ ____ = _____
Use the above system of equations to determine how many adult and student tickets were sold.
_____ adult tickets and ____ student tickets were sold.
Answers:
380, 2.50, 4, 309, s, 2820, 900, 6.5, 591, 510, a 390, 520.

3 answers

Let's break down the provided information into equations.

  1. First equation for total sales: The total revenue from ticket sales is given as $2,820. Adult tickets cost $4 (each) and student tickets cost $2.50 (each), and we will use the variables \( a \) for adult tickets and \( s \) for student tickets.

    The equation can be set up as: \[ 4a + 2.5s = 2820 \]

  2. Second equation for total tickets sold: The total number of tickets sold (both adult and student) is 900. This can be expressed as: \[ a + s = 900 \]

Now we have a system of equations:

  1. \( 4a + 2.5s = 2820 \) (Total revenue)
  2. \( a + s = 900 \) (Total tickets sold)

Now, let's solve the system of equations.

From the second equation, we can express \( s \) in terms of \( a \): \[ s = 900 - a \]

Now, substitute this expression for \( s \) into the first equation: \[ 4a + 2.5(900 - a) = 2820 \]

Distributing \( 2.5 \): \[ 4a + 2250 - 2.5a = 2820 \]

Combining like terms: \[ (4 - 2.5)a + 2250 = 2820 \] \[ 1.5a + 2250 = 2820 \]

Subtracting 2250 from both sides: \[ 1.5a = 570 \]

Now, divide by 1.5: \[ a = \frac{570}{1.5} = 380 \]

Now that we have the number of adult tickets sold, substitute \( a \) back into the equation for \( s \): \[ s = 900 - 380 = 520 \]

Summary of the Results:

  • Adult tickets sold: \( 380 \)
  • Student tickets sold: \( 520 \)

Final Equations:

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

Answers:

  • \( 4, 2.5, 2820, 900 \)
  • Adult tickets sold: 380
  • Student tickets sold: 520
are you sure?

Let's double-check the calculations step-by-step to ensure everything is correct.

Given:

  1. Adult tickets cost $4, so revenue from adult tickets is \( 4a \).
  2. Student tickets cost $2.50, so revenue from student tickets is \( 2.5s \).
  3. Total revenue is $2,820.
  4. Total tickets sold is 900.

Step 1: Write the equations

  1. Total revenue equation: \[ 4a + 2.5s = 2820 \]

  2. Total tickets sold equation: \[ a + s = 900 \]

Step 2: Solve the system of equations

From the second equation: \[ s = 900 - a \]

Substitute \( s \) into the revenue equation

Replace \( s \) in the first equation: \[ 4a + 2.5(900 - a) = 2820 \]

Distributing \( 2.5 \): \[ 4a + 2250 - 2.5a = 2820 \]

Combine like terms: \[ (4 - 2.5)a + 2250 = 2820 \] \[ 1.5a + 2250 = 2820 \]

Step 3: Solve for \( a \)

Subtract 2250 from both sides: \[ 1.5a = 2820 - 2250 \] \[ 1.5a = 570 \]

Now divide by 1.5: \[ a = \frac{570}{1.5} \]

Calculating this, \[ a = 380 \]

Step 4: Solve for \( s \)

Now, substitute \( a \) back into the equation for \( s \): \[ s = 900 - 380 \] \[ s = 520 \]

Final Verification:

  • Adult tickets sold: 380
  • Student tickets sold: 520

Check:

  1. Verify revenue: \[ 4(380) + 2.5(520) = 1520 + 1300 = 2820 \quad \text{(Correct)} \]

  2. Verify total tickets: \[ 380 + 520 = 900 \quad \text{(Correct)} \]

So the calculations are indeed correct. The number of adult tickets sold is 380, and the number of student tickets sold is 520.