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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

Let's denote the number of adults as \( A \) and the number of children as \( C \).

We have two equations based on the information provided:

  1. The total number of attendees:
    \[ A + C = 500 \]

  2. The total revenue from admissions:
    \[ 10A + 5C = 3500 \]

Now we can solve these equations step by step.

Step 1: Solve for \( C \) in terms of \( A \)

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

Step 2: Substitute \( C \) in the second equation

Now we substitute \( C \) in the second equation: \[ 10A + 5(500 - A) = 3500 \]

Distribute the \( 5 \): \[ 10A + 2500 - 5A = 3500 \]

Combine like terms: \[ 5A + 2500 = 3500 \]

Step 3: Isolate \( A \)

Subtract \( 2500 \) from both sides: \[ 5A = 1000 \]

Now divide by \( 5 \): \[ A = 200 \]

Step 4: Calculate \( C \)

Now that we have \( A \), we can find \( C \): \[ C = 500 - A = 500 - 200 = 300 \]

Summary

Thus, the number of adults and children needed to attend to reach the goal of $3,500 is:

  • 200 adults
  • 300 children

Final answer: 200 adults; 300 children.