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The Kesling Middle School PTA is planning a carnival to raise money for the school’s art department. They estimate that the event will be very popular and that they will have 500 people attend. They plan to charge adults $10 and children $5 for admission. The PTA wants to earn $3,500 from admission charges. How many adults and how many children need to attend for the PTA to reach their goal of $3,500?(1 point)

adults; children

1 answer

To find the number of adults and children needed to attend the carnival to reach the goal of $3,500, we can set up a system of equations.

Let:

  • \( x \) = number of adults
  • \( y \) = number of children

From the problem, we have the following equations based on the given information:

  1. The total number of attendees is 500: \[ x + y = 500 \]

  2. The total revenue needed is $3,500. Since adults are charged $10 and children $5: \[ 10x + 5y = 3500 \]

Now we can solve this system of equations.

Step 1: Solve the first equation for one variable.

From the first equation, we can express \( y \) in terms of \( x \): \[ y = 500 - x \]

Step 2: Substitute into the second equation.

Now, substitute \( y \) in the second equation: \[ 10x + 5(500 - x) = 3500 \] Expanding this, we get: \[ 10x + 2500 - 5x = 3500 \] Combining like terms: \[ 5x + 2500 = 3500 \] Subtracting 2500 from both sides: \[ 5x = 1000 \] Dividing by 5: \[ x = 200 \]

Step 3: Find \( y \).

Now substitute \( x = 200 \) back into the equation for \( y \): \[ y = 500 - 200 = 300 \]

Thus, to reach the goal of $3,500, the PTA needs 200 adults and 300 children to attend the carnival.

Final answer: 200 adults; 300 children